Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $σ_{\min}$, at which the score is stiff and the flow develops a boundary layer. We treat $σ_{\min}$ as a singular-perturbation parameter and determine which fixed-step samplers are asymptotic-preserving (AP), that is, stable and uniformly accurate as $σ_{\min}\to0$, casting the criteria as an a posteriori audit: residual functionals with $σ_{\min}$-uniform coefficients, computable on a pretrained checkpoint without ground-truth scores or exact trajectories. On the terminal layer, Euler in the $σ$-clock, the deterministic DDIM update, is the unique layer-exact discretization up to affine reparameterization, with rectified flow its flow-matching counterpart; the $λ$-clock is stable only for steps $h\le h_\star=1+W(1/e)$, and the uniform-$σ^2$ heat clock stalls a $σ_{\min}$-independent distance from the data. On two solvable models (rank-deficient Gaussian, symmetric two-point mixture), deterministic samplers remain first-order uniformly accurate with no $\log(1/σ_{\min})$ factor, even across a symmetric posterior-switching interface whose distributional budget is a universal constant; the logarithm is charged entirely to the Itô term of stochastic samplers, whose path-KL scales as $Λ^2/N$ against the ODE's $O(Λ^2/N^2)$ budget, with $Λ=\log(σ_{\max}/σ_{\min})$. On the EDM CIFAR-10 checkpoint, spectra measured once predict held-out residual budgets across step count, schedule, and noise level against pre-specified gates with no per-configuration refitting, and calibrate the Itô coefficient at $M_1=1.00\pm0.01$. The clock decides stability; the noise, not the geometry, charges the logarithm.
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Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $σ_{\min}$, at which the score is stiff and the flow develops a boundary layer. We treat $σ_{\min}$ as a singular-perturbation parameter and determine which fixed-step samplers are asymptotic-preserving (AP), that is, stable and uniformly accurate as $σ_{\min}\to0$, casting the criteria as an a posteriori audit: residual functionals with $σ_{\min}$-uniform coefficients, computable on a pretrained checkpoint without ground-truth scores or exact trajectories. On the terminal layer, Euler in the $σ$-clock, the deterministic DDIM update, is the unique layer-exact discretization up to affine reparameterization, with rectified flow its flow-matching counterpart; the $λ$-clock is stable only for steps $h\le h_\star=1+W(1/e)$, and the uniform-$σ^2$ heat clock stalls a $σ_{\min}$-independent distance from the data. On two solvable models (rank-deficient Gaussian, symmetric two-point mixture), deterministic samplers remain first-order uniformly accurate with no $\log(1/σ_{\min})$ factor, even across a symmetric posterior-switching interface whose distributional budget is a universal constant; the logarithm is charged entirely to the Itô term of stochastic samplers, whose path-KL scales as $Λ^2/N$ against the ODE's $O(Λ^2/N^2)$ budget, with $Λ=\log(σ_{\max}/σ_{\min})$. On the EDM CIFAR-10 checkpoint, spectra measured once predict held-out residual budgets across step count, schedule, and noise level against pre-specified gates with no per-configuration refitting, and calibrate the Itô coefficient at $M_1=1.00\pm0.01$. The clock decides stability; the noise, not the geometry, charges the logarithm.
Discrete diffusion promises orders-of-magnitude faster generation than autoregressive (AR) models for sequential discrete data, yet its full potential of few-step generation has remained out of reach due to a fundamental structural limitation. The conditional-independence assumption underlying current discrete diffusion models introduces a systematic parallelization bias that compounds with the number of tokens unmasked per step, becoming severe in the few-step regime that fast generation requires. We address this with the first framework for explicit joint distribution modeling in discrete diffusion via tensor decomposition, which represents the conditional clean distribution as a low-rank tensor with controllable expressivity. The framework supports both Canonical Polyadic (CPD) and Tensor-Train (TTD) decompositions, and we identify a structural bias of TTD toward dependencies between nearby tokens, formalized through Oseledets' theorem relating TT-rank to unfolding-matrix rank, which is well-suited to sequential data such as natural language and line notations for molecular data. To enable efficient generation, we present an iterative marginal inference procedure with specialization for predetermined position schedules. Our framework integrates into pretrained MDMs through lightweight fine-tuning, yielding substantial improvements in few-step generation at a fraction of the cost of training from scratch.
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Discrete diffusion promises orders-of-magnitude faster generation than autoregressive (AR) models for sequential discrete data, yet its full potential of few-step generation has remained out of reach due to a fundamental structural limitation. The conditional-independence assumption underlying current discrete diffusion models introduces a systematic parallelization bias that compounds with the number of tokens unmasked per step, becoming severe in the few-step regime that fast generation requires. We address this with the first framework for explicit joint distribution modeling in discrete diffusion via tensor decomposition, which represents the conditional clean distribution as a low-rank tensor with controllable expressivity. The framework supports both Canonical Polyadic (CPD) and Tensor-Train (TTD) decompositions, and we identify a structural bias of TTD toward dependencies between nearby tokens, formalized through Oseledets' theorem relating TT-rank to unfolding-matrix rank, which is well-suited to sequential data such as natural language and line notations for molecular data. To enable efficient generation, we present an iterative marginal inference procedure with specialization for predetermined position schedules. Our framework integrates into pretrained MDMs through lightweight fine-tuning, yielding substantial improvements in few-step generation at a fraction of the cost of training from scratch.
Minimum maximum mean discrepancy (MMD) estimation has emerged as a robust and likelihood-free alternative to maximum likelihood estimation for parameter estimation. Yet, despite its practical success, the associated optimization problem remains poorly understood, with theoretical guarantees for existing algorithms hinging on convexity assumptions that rarely hold in practice. We address this gap by proposing a preconditioned gradient descent (PGD) scheme, establishing its asymptotic global convergence under explicit gradient-dominance and projection-residual conditions. Our approach is inspired by recent progress on MMD gradient flows, a nonparametric descent scheme on the space of probability measures. We provide extensive empirical evidence that our PGD scheme outperforms standard gradient descent across a range of challenging parameter estimation and composite hypothesis testing problems.
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Minimum maximum mean discrepancy (MMD) estimation has emerged as a robust and likelihood-free alternative to maximum likelihood estimation for parameter estimation. Yet, despite its practical success, the associated optimization problem remains poorly understood, with theoretical guarantees for existing algorithms hinging on convexity assumptions that rarely hold in practice. We address this gap by proposing a preconditioned gradient descent (PGD) scheme, establishing its asymptotic global convergence under explicit gradient-dominance and projection-residual conditions. Our approach is inspired by recent progress on MMD gradient flows, a nonparametric descent scheme on the space of probability measures. We provide extensive empirical evidence that our PGD scheme outperforms standard gradient descent across a range of challenging parameter estimation and composite hypothesis testing problems.
Precise control over complex dynamics remains challenging for modern video generative models, as text prompts alone often cannot specify physically plausible, fine-grained motion and interactions. We introduce $proxy-conditioned video generation$, where a coarse proxy video from physics-based simulation or real-world recording serves as a dynamics carrier to control foreground object motion. Given a proxy video and a text prompt, the goal is to synthesize a new video that preserves the proxy dynamics while generating novel content and plausible interactions aligned with the prompt. Since paired proxy-target videos are difficult to obtain, we propose $ProxyUp$, a training-free framework built on pretrained video generative models. ProxyUp first inverts the proxy video into an intermediate latent representation and applies $region-wise latent noising$, preserving motion-critical proxy latents while injecting noise into regions intended for text-driven regeneration. To mitigate the distribution mismatch and weak foreground-background coupling introduced by this heuristic latent composition, we further propose $Stochastic Flow Relaxation (SFR)$, which progressively relaxes the composed latent toward the model's learned distribution before ODE sampling. Experiments on both simulation and real-world proxies show that ProxyUp outperforms strong video editing and motion transfer baselines in dynamic fidelity and text alignment.
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Precise control over complex dynamics remains challenging for modern video generative models, as text prompts alone often cannot specify physically plausible, fine-grained motion and interactions. We introduce $proxy-conditioned video generation$, where a coarse proxy video from physics-based simulation or real-world recording serves as a dynamics carrier to control foreground object motion. Given a proxy video and a text prompt, the goal is to synthesize a new video that preserves the proxy dynamics while generating novel content and plausible interactions aligned with the prompt. Since paired proxy-target videos are difficult to obtain, we propose $ProxyUp$, a training-free framework built on pretrained video generative models. ProxyUp first inverts the proxy video into an intermediate latent representation and applies $region-wise latent noising$, preserving motion-critical proxy latents while injecting noise into regions intended for text-driven regeneration. To mitigate the distribution mismatch and weak foreground-background coupling introduced by this heuristic latent composition, we further propose $Stochastic Flow Relaxation (SFR)$, which progressively relaxes the composed latent toward the model's learned distribution before ODE sampling. Experiments on both simulation and real-world proxies show that ProxyUp outperforms strong video editing and motion transfer baselines in dynamic fidelity and text alignment.
Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables: similar activity can emerge from coordinated parameter changes. We formalize these compatible parameter sets as viable parameter manifolds: the inverse images of a system's target dynamical behaviors under a parameter-to-feature map. The relevant codimension is not the number of reported features, but the effective rank of that map at the target scale. Co-varying features lower the codimension, while poor conditioning, high curvature, or regime mixing degrade learnability. We train conditional score-based diffusion models on simulated parameter--feature pairs and use them as amortized samplers of prior-weighted viable sets. In the Lorenz system, scalar trajectory statistics generate thin viable sheets, and two-feature conditioning localizes a transition-adjacent corridor. In the Izhikevich neuron model, four firing descriptors lie close to a nearly two-dimensional family of features, and the learned inverse images reveal distinct regular and irregular compensation geometries. In a recent ODE reduction of finite spiking networks, the same framework reveals excitatory--inhibitory compensation, timescale--coupling tradeoffs, and input-dependent viable manifolds across 4--12 parameter dimensions. In this view, robustness, compensation, and hidden parameter dependencies are organized as inverse geometry, with diffusion models providing practical tools for sampling, visualizing, and interrogating that geometry.
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Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables: similar activity can emerge from coordinated parameter changes. We formalize these compatible parameter sets as viable parameter manifolds: the inverse images of a system's target dynamical behaviors under a parameter-to-feature map. The relevant codimension is not the number of reported features, but the effective rank of that map at the target scale. Co-varying features lower the codimension, while poor conditioning, high curvature, or regime mixing degrade learnability. We train conditional score-based diffusion models on simulated parameter--feature pairs and use them as amortized samplers of prior-weighted viable sets. In the Lorenz system, scalar trajectory statistics generate thin viable sheets, and two-feature conditioning localizes a transition-adjacent corridor. In the Izhikevich neuron model, four firing descriptors lie close to a nearly two-dimensional family of features, and the learned inverse images reveal distinct regular and irregular compensation geometries. In a recent ODE reduction of finite spiking networks, the same framework reveals excitatory--inhibitory compensation, timescale--coupling tradeoffs, and input-dependent viable manifolds across 4--12 parameter dimensions. In this view, robustness, compensation, and hidden parameter dependencies are organized as inverse geometry, with diffusion models providing practical tools for sampling, visualizing, and interrogating that geometry.
作者Chaoqun Wang, Yuehuan Wei, Haoxiang Cao, Shaobo Min
Single-image reflection removal (SIRR) aims to recover the clean transmission layer from a reflection-contaminated image. Although recent methods achieve promising results with large diffusion models, they rely on image-agnostic adaptation strategies, e.g., fine-tuning or ControlNet, that enforce uniform suppression regardless of reflection severity. As a result, heavy reflections often leave residuals, while weak ones suffer from detail loss. To this end, we propose ReLo-IRR, a reflection-guided LoRA framework built upon the rectified flow model. First, a lightweight estimator is designed to predict the reflection strength descriptor, providing an explicit prior of reflection dominance for each image and enabling image-dependent LoRA modulation. Second, we introduce a time-conditioned mechanism that fuses this reflection descriptor with timestep embeddings, enabling LoRA modulation to evolve consistently with the coarse-to-fine denoising process. By jointly modeling reflection strength and denoising dynamics, our ReLo-IRR achieves robust suppression of diverse reflection conditions. Extensive experiments on challenging benchmarks validate the effectiveness of ReLo-IRR, demonstrating superior dereflection performance and robust generalization. The code is released at https://github.com/KONGBAI-8080/ReLo-IRR.
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Single-image reflection removal (SIRR) aims to recover the clean transmission layer from a reflection-contaminated image. Although recent methods achieve promising results with large diffusion models, they rely on image-agnostic adaptation strategies, e.g., fine-tuning or ControlNet, that enforce uniform suppression regardless of reflection severity. As a result, heavy reflections often leave residuals, while weak ones suffer from detail loss. To this end, we propose ReLo-IRR, a reflection-guided LoRA framework built upon the rectified flow model. First, a lightweight estimator is designed to predict the reflection strength descriptor, providing an explicit prior of reflection dominance for each image and enabling image-dependent LoRA modulation. Second, we introduce a time-conditioned mechanism that fuses this reflection descriptor with timestep embeddings, enabling LoRA modulation to evolve consistently with the coarse-to-fine denoising process. By jointly modeling reflection strength and denoising dynamics, our ReLo-IRR achieves robust suppression of diverse reflection conditions. Extensive experiments on challenging benchmarks validate the effectiveness of ReLo-IRR, demonstrating superior dereflection performance and robust generalization. The code is released at https://github.com/KONGBAI-8080/ReLo-IRR.
Real-time cardiac cine MRI enables visualization of the beating heart during free breathing, but severe undersampling and motion make reconstruction highly challenging. A central challenge for reconstruction is incorporating powerful priors of cardiac anatomy while remaining computationally efficient. We propose Piecewise Dynamic Diffusion Regularization (PDDR), a reconstruction method that integrates a spatiotemporal diffusion model as a generative prior within a variational reconstruction framework for cine MRI. The model employs dedicated spatial layers to encode anatomical structure and temporal layers to capture cardiac motion learned from gated cine data. PDDR leverages the dynamic prior in a piecewise manner, enabling the efficient use of spatiotemporal diffusion models for processing of long real-time sequences. Experiments on retrospectively accelerated and prospective real-time cine MRI demonstrate that PDDR outperforms classical, unsupervised, and diffusion-based methods, delivering high-quality reconstructions with substantially reduced computation time compared to state-of-the-art baselines. These results highlight PDDR as a practical and scalable solution for free-breathing, real-time cardiac MRI. Code is available at https://github.com/MLI-lab/pddr.
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Real-time cardiac cine MRI enables visualization of the beating heart during free breathing, but severe undersampling and motion make reconstruction highly challenging. A central challenge for reconstruction is incorporating powerful priors of cardiac anatomy while remaining computationally efficient. We propose Piecewise Dynamic Diffusion Regularization (PDDR), a reconstruction method that integrates a spatiotemporal diffusion model as a generative prior within a variational reconstruction framework for cine MRI. The model employs dedicated spatial layers to encode anatomical structure and temporal layers to capture cardiac motion learned from gated cine data. PDDR leverages the dynamic prior in a piecewise manner, enabling the efficient use of spatiotemporal diffusion models for processing of long real-time sequences. Experiments on retrospectively accelerated and prospective real-time cine MRI demonstrate that PDDR outperforms classical, unsupervised, and diffusion-based methods, delivering high-quality reconstructions with substantially reduced computation time compared to state-of-the-art baselines. These results highlight PDDR as a practical and scalable solution for free-breathing, real-time cardiac MRI. Code is available at https://github.com/MLI-lab/pddr.
作者Emmanuel Bengio, Sanjeev Raja, Yui Tik Pang, Kerstin Klaeser, Cristian Gabellini, Nikhil Shenoy, Francesco Di Giovanni, Prudencio Tossou
We present AquaGen, the first all-atom, explicit solvent, periodic-boundary-condition-aware generative model that produces molecular configurations from the Boltzmann distribution at a fraction of the cost of molecular dynamics (MD). This is in contrast with existing generative models that remove degrees of freedom by operating on coarse-grained, vacuum, or implicit solvent systems. Operating at this resolution allows for post-processing through force field energy evaluations and MD simulations, and enables the prediction of relevant properties in a gray-box manner (as ensemble averages of potential energy evaluations over generated samples). We demonstrate the utility of this paradigm on absolute hydration free energy (AHFE), producing estimates 4-10x faster and with comparable accuracy to standard GPU-based MD. By generating uncorrelated samples from alchemical Boltzmann distributions, we create more accurate, interpretable, and refinable ensemble predictions with calibrated uncertainty estimates, unlike regression methods which are entirely black-box predictors. Our approach also yields predictable benefits from increasing train- and test-time compute, realized by scaling model size and generating more samples, respectively. We believe that this approach demonstrates the utility of high-resolution ensemble generation for free energy estimation, with future potential to replace MD in tasks such as the prediction of lipophilicity, membrane permeability, or absolute binding free energy (ABFE) — whose grounding and interpretability may be critical for the development of new drugs and materials.
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We present AquaGen, the first all-atom, explicit solvent, periodic-boundary-condition-aware generative model that produces molecular configurations from the Boltzmann distribution at a fraction of the cost of molecular dynamics (MD). This is in contrast with existing generative models that remove degrees of freedom by operating on coarse-grained, vacuum, or implicit solvent systems. Operating at this resolution allows for post-processing through force field energy evaluations and MD simulations, and enables the prediction of relevant properties in a gray-box manner (as ensemble averages of potential energy evaluations over generated samples). We demonstrate the utility of this paradigm on absolute hydration free energy (AHFE), producing estimates 4-10x faster and with comparable accuracy to standard GPU-based MD. By generating uncorrelated samples from alchemical Boltzmann distributions, we create more accurate, interpretable, and refinable ensemble predictions with calibrated uncertainty estimates, unlike regression methods which are entirely black-box predictors. Our approach also yields predictable benefits from increasing train- and test-time compute, realized by scaling model size and generating more samples, respectively. We believe that this approach demonstrates the utility of high-resolution ensemble generation for free energy estimation, with future potential to replace MD in tasks such as the prediction of lipophilicity, membrane permeability, or absolute binding free energy (ABFE) — whose grounding and interpretability may be critical for the development of new drugs and materials.
Diffusion architectures now encompass convolutional UNets as well as transformer-based designs such as Diffusion Transformers (DiTs), inspired by Vision Transformers (ViTs), yet the effects of structured geometric perturbations within these architectures remain poorly understood. We study this question through a unified framework that applies reflection-based elements of the dihedral group to intermediate hidden states as controlled internal interventions, contrasting geometrically consistent and inconsistent variants. Using activation-level diagnostics, including Self-Consistency Shift (SCS), Activation Mass Scatter (AMS), and Drift, we analyze feature stability and geometric drift. We find that consistent transformations improve stability, while inconsistent ones induce predictable, architecture-specific failures. In the main Stable Diffusion 2.1 U-Net study, we evaluate seven intervention modes over three seeds and complement the internal diagnostics with image-level FID, KID, CLIP score, and LPIPS diversity. Taken together with supporting ViT and controlled DiT analyses, these results establish geometric consistency as a key principle for stable hidden-state interventions in spatially structured vision and diffusion models.
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Diffusion architectures now encompass convolutional UNets as well as transformer-based designs such as Diffusion Transformers (DiTs), inspired by Vision Transformers (ViTs), yet the effects of structured geometric perturbations within these architectures remain poorly understood. We study this question through a unified framework that applies reflection-based elements of the dihedral group to intermediate hidden states as controlled internal interventions, contrasting geometrically consistent and inconsistent variants. Using activation-level diagnostics, including Self-Consistency Shift (SCS), Activation Mass Scatter (AMS), and Drift, we analyze feature stability and geometric drift. We find that consistent transformations improve stability, while inconsistent ones induce predictable, architecture-specific failures. In the main Stable Diffusion 2.1 U-Net study, we evaluate seven intervention modes over three seeds and complement the internal diagnostics with image-level FID, KID, CLIP score, and LPIPS diversity. Taken together with supporting ViT and controlled DiT analyses, these results establish geometric consistency as a key principle for stable hidden-state interventions in spatially structured vision and diffusion models.
The accuracy of consumer-grade inertial navigation is bottlenecked by the stochastic noise of Micro-Electro-Mechanical Systems (MEMS). Traditional deterministic neural architectures often succumb to ``estimation jittering,'' sacrificing high-frequency kinematic fidelity for numerical stability. We propose PedestrianDiffusion, a multimodal spectral-domain generative framework reformulating dense 6D state estimation as a continuous conditional denoising process. By operating in the frequency domain, our formulation bounds the spectral covariance, acting as a mathematical preconditioner to stabilize the reverse diffusion trajectory. Furthermore, we introduce a zero-shot semantic conditioning mechanism leveraging vision-language embeddings as categorical priors to generalize across heterogeneous sensor noise profiles. To address the computational intractability of generative tracking, we deploy a single-step deterministic probability flow ODE solver ($T=1$). This yields high-capacity asynchronous batch trajectory refinement, establishing the viability of generative architectures for asynchronous batch trajectory refinement on edge hardware. Extensive evaluations on the OxIOD, RIDI, RoNIN, and TLIO benchmarks demonstrate that PedestrianDiffusion achieves state-of-the-art performance, exhibiting unprecedented robustness to impulse perturbations and coupled 6D kinematic drift. This work provides a rigorous algorithmic blueprint for next-generation Neural Inertial Measurement Units (N-IMUs).
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The accuracy of consumer-grade inertial navigation is bottlenecked by the stochastic noise of Micro-Electro-Mechanical Systems (MEMS). Traditional deterministic neural architectures often succumb to ``estimation jittering,'' sacrificing high-frequency kinematic fidelity for numerical stability. We propose PedestrianDiffusion, a multimodal spectral-domain generative framework reformulating dense 6D state estimation as a continuous conditional denoising process. By operating in the frequency domain, our formulation bounds the spectral covariance, acting as a mathematical preconditioner to stabilize the reverse diffusion trajectory. Furthermore, we introduce a zero-shot semantic conditioning mechanism leveraging vision-language embeddings as categorical priors to generalize across heterogeneous sensor noise profiles. To address the computational intractability of generative tracking, we deploy a single-step deterministic probability flow ODE solver ($T=1$). This yields high-capacity asynchronous batch trajectory refinement, establishing the viability of generative architectures for asynchronous batch trajectory refinement on edge hardware. Extensive evaluations on the OxIOD, RIDI, RoNIN, and TLIO benchmarks demonstrate that PedestrianDiffusion achieves state-of-the-art performance, exhibiting unprecedented robustness to impulse perturbations and coupled 6D kinematic drift. This work provides a rigorous algorithmic blueprint for next-generation Neural Inertial Measurement Units (N-IMUs).
Text-to-Image diffusion models often propagate harmful bias inherited from the training data. Existing bias mitigation techniques typically intervene only at the text encoder or provide inference-time guidance, often leading to generations that collapse into semantically incoherent outputs. To address these limitations, we introduce CO-ALIGN (Concept Ontology Alignment), a novel bias mitigation approach based on concept-graph alignment that operates on the model's internal concept ontology. By aligning concepts within the text encoder and denoiser, CO-ALIGN achieves substantial bias reduction while preserving generative integrity. We demonstrate the effectiveness of concept-graph alignment across three paradigms: text-encoders, denoisers and joint text-denoiser ontology alignment. CO-ALIGN outperforms the state of the art, improving fairness by $30%$, $ΔFID=11.4$ in image quality, $2.8%$ in image fidelity, all while reducing semantically incoherent outputs by $88%$. Beyond bias mitigation, we show that CO-ALIGN benefits other downstream tasks as well. In particular, our experiments demonstrate that better-aligned internal ontologies enhance concept unlearning robustness across multiple unlearning techniques.
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Text-to-Image diffusion models often propagate harmful bias inherited from the training data. Existing bias mitigation techniques typically intervene only at the text encoder or provide inference-time guidance, often leading to generations that collapse into semantically incoherent outputs. To address these limitations, we introduce CO-ALIGN (Concept Ontology Alignment), a novel bias mitigation approach based on concept-graph alignment that operates on the model's internal concept ontology. By aligning concepts within the text encoder and denoiser, CO-ALIGN achieves substantial bias reduction while preserving generative integrity. We demonstrate the effectiveness of concept-graph alignment across three paradigms: text-encoders, denoisers and joint text-denoiser ontology alignment. CO-ALIGN outperforms the state of the art, improving fairness by $30%$, $ΔFID=11.4$ in image quality, $2.8%$ in image fidelity, all while reducing semantically incoherent outputs by $88%$. Beyond bias mitigation, we show that CO-ALIGN benefits other downstream tasks as well. In particular, our experiments demonstrate that better-aligned internal ontologies enhance concept unlearning robustness across multiple unlearning techniques.
作者Jiawei Sheng, Taoyu Su, Xixun Lin, Xiaodong Li, Tingwen Liu
Multi-domain knowledge graph completion (MKGC) aims to improve missing triple prediction in a target KG by transferring knowledge from other support KGs. Existing methods typically enforce consistency constraints on equivalent entities across KGs to transfer knowledge, which risks suppressing domain-specific contextual information of entities. This design can also compromise entity representation information from all KG domains, impeding performance improvements, especially in low-resource data scenarios. To address this, we pioneer a generation-based paradigm for MKGC and propose DMKGC, a conditional diffusion-guided knowledge transfer framework. Our key insight is to treat each KG as a partial view of the entity entire information, and generate informative domain-general entity embeddings through diffusion models conditioned on support KGs. Particularly, we first initialize domain-agnostic entity embeddings as prior entity embeddings, and then encode them within individual KGs. Afterward, we fuse equivalent entities from support KGs as the conditional diffusion generation guidance. We leverage the prior entity embeddings as the proxy generation objective, which ensures this conditional generation to be unbiased towards any conditioned KGs. Simultaneously, we also train the generated embeddings to be predictive across KGs, thus preserving domain-specific information. Extensive experiments on 14 KGs in 3 benchmarks demonstrate a 4.3% average MRR improvement in tail entity prediction over state-of-the-art methods, with sustained gains in low-resource data settings.
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Multi-domain knowledge graph completion (MKGC) aims to improve missing triple prediction in a target KG by transferring knowledge from other support KGs. Existing methods typically enforce consistency constraints on equivalent entities across KGs to transfer knowledge, which risks suppressing domain-specific contextual information of entities. This design can also compromise entity representation information from all KG domains, impeding performance improvements, especially in low-resource data scenarios. To address this, we pioneer a generation-based paradigm for MKGC and propose DMKGC, a conditional diffusion-guided knowledge transfer framework. Our key insight is to treat each KG as a partial view of the entity entire information, and generate informative domain-general entity embeddings through diffusion models conditioned on support KGs. Particularly, we first initialize domain-agnostic entity embeddings as prior entity embeddings, and then encode them within individual KGs. Afterward, we fuse equivalent entities from support KGs as the conditional diffusion generation guidance. We leverage the prior entity embeddings as the proxy generation objective, which ensures this conditional generation to be unbiased towards any conditioned KGs. Simultaneously, we also train the generated embeddings to be predictive across KGs, thus preserving domain-specific information. Extensive experiments on 14 KGs in 3 benchmarks demonstrate a 4.3% average MRR improvement in tail entity prediction over state-of-the-art methods, with sustained gains in low-resource data settings.
作者Trevor Chen, Ariel Dai, Jason Yang, Riccardo De Santi, Daniel Khalil, Wenda Chu, Nate Gruver, Pranav Murugan, Alexander F. G. Goldberg, Maruan Al-Shedivat, Yisong Yue
Molecular optimization often starts from a pretrained generative model that captures a broad prior over valid molecular structures. At test time, however, the goal is not to sample from this prior, but to use a limited oracle budget to shift generation toward task-specific high-reward molecules. We study this adaptation problem for discrete diffusion models. Each online round couples several choices. The loop must decide which candidates to evaluate, how rewards become model updates, which feedback to reuse, and how far to move beyond the pretrained prior. These choices have mostly been studied in isolation, leaving open whether they complement one another, become redundant, or interfere inside a full online adaptation loop. We conduct controlled studies across six small-molecule binding-affinity tasks and three protein-fitness tasks. We find that acquisition, reward shaping, and model debiasing provide complementary routes to higher reward, especially for small molecules. Replay further stabilizes learning, while validity penalties keep small-molecule exploration on the valid molecular manifold. Together, these findings point to a practical recipe for feedback-efficient molecular optimization: online fine-tuning with acquisition, reward shaping, debiasing, replay, and validity control. This recipe outperforms offline fine-tuning and inference-time search baselines under matched oracle-call budgets and GPU-hour accounting. The gains are largest when high-reward candidates require larger shifts from the pretrained prior.
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Molecular optimization often starts from a pretrained generative model that captures a broad prior over valid molecular structures. At test time, however, the goal is not to sample from this prior, but to use a limited oracle budget to shift generation toward task-specific high-reward molecules. We study this adaptation problem for discrete diffusion models. Each online round couples several choices. The loop must decide which candidates to evaluate, how rewards become model updates, which feedback to reuse, and how far to move beyond the pretrained prior. These choices have mostly been studied in isolation, leaving open whether they complement one another, become redundant, or interfere inside a full online adaptation loop. We conduct controlled studies across six small-molecule binding-affinity tasks and three protein-fitness tasks. We find that acquisition, reward shaping, and model debiasing provide complementary routes to higher reward, especially for small molecules. Replay further stabilizes learning, while validity penalties keep small-molecule exploration on the valid molecular manifold. Together, these findings point to a practical recipe for feedback-efficient molecular optimization: online fine-tuning with acquisition, reward shaping, debiasing, replay, and validity control. This recipe outperforms offline fine-tuning and inference-time search baselines under matched oracle-call budgets and GPU-hour accounting. The gains are largest when high-reward candidates require larger shifts from the pretrained prior.
作者Binglin Ji, Anindya Sarkar, Hengchang Lu, Jens Sjölund, Yevgeniy Vorobeychik
In many scientific and engineering domains, maximizing discovery within a limited sampling budget demands strategic, observation-guided exploration. While generative models have enabled training-free reward alignment, current methods typically excel in local searches within narrow regions of the underlying distribution. These approaches struggle when preferences are unknown a priori and only revealed through sequential feedback-a scenario demanding broad exploration to uncover high-utility regions. To address this, we introduce Bootstrap Flow-Map-Tree (a.k.a BFMT), a novel computationally efficient sampling framework designed for history-aware global search and alignment under sampling budget constraints. BFMT enables full tree-path construction from any tree depth using a single function evaluation, drastically reducing computational overhead while providing critical foresight for sequential sampling. By enabling dynamic transition time steps scheduling, BFMT efficiently allocates its sampling budget, smoothly transitioning from broad global exploration to fine-grained local refinement of high-utility modes discovered through exploration. Extensive experiments and ablations across diverse search and alignment tasks demonstrate that BFMT substantially outperforms baseline approaches.
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In many scientific and engineering domains, maximizing discovery within a limited sampling budget demands strategic, observation-guided exploration. While generative models have enabled training-free reward alignment, current methods typically excel in local searches within narrow regions of the underlying distribution. These approaches struggle when preferences are unknown a priori and only revealed through sequential feedback-a scenario demanding broad exploration to uncover high-utility regions. To address this, we introduce Bootstrap Flow-Map-Tree (a.k.a BFMT), a novel computationally efficient sampling framework designed for history-aware global search and alignment under sampling budget constraints. BFMT enables full tree-path construction from any tree depth using a single function evaluation, drastically reducing computational overhead while providing critical foresight for sequential sampling. By enabling dynamic transition time steps scheduling, BFMT efficiently allocates its sampling budget, smoothly transitioning from broad global exploration to fine-grained local refinement of high-utility modes discovered through exploration. Extensive experiments and ablations across diverse search and alignment tasks demonstrate that BFMT substantially outperforms baseline approaches.
Recovering online pen trajectories from offline handwriting images, often referred to as handwriting trajectory recovery (stroke recovery), is an offline-to-online conversion task with applications in stroke-level editing and forensic analysis. We propose, to the best of our knowledge, the first diffusion-model-based framework for this task. Our method formulates trajectory recovery as image-conditioned generation and uses a denoising diffusion model to sample pen trajectories consistent with the observed ink trace. Through extensive quantitative evaluations on CASIA-OLHWDB (1.0-1.1), we verify that the proposed approach enables accurate recovery even for complex multi-stroke characters, substantially improving both temporal similarity (DTW/LDTW) and shape fidelity (AIoU) over representative prior methods such as PEN-Net and Cross-VAE. We further show that the model captures general stroke-order tendencies and generalizes to classes unseen during training, exemplified by cross-script transfer: a model trained on Chinese characters can recover reasonable stroke orders for Latin letters to some extent.
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Recovering online pen trajectories from offline handwriting images, often referred to as handwriting trajectory recovery (stroke recovery), is an offline-to-online conversion task with applications in stroke-level editing and forensic analysis. We propose, to the best of our knowledge, the first diffusion-model-based framework for this task. Our method formulates trajectory recovery as image-conditioned generation and uses a denoising diffusion model to sample pen trajectories consistent with the observed ink trace. Through extensive quantitative evaluations on CASIA-OLHWDB (1.0-1.1), we verify that the proposed approach enables accurate recovery even for complex multi-stroke characters, substantially improving both temporal similarity (DTW/LDTW) and shape fidelity (AIoU) over representative prior methods such as PEN-Net and Cross-VAE. We further show that the model captures general stroke-order tendencies and generalizes to classes unseen during training, exemplified by cross-script transfer: a model trained on Chinese characters can recover reasonable stroke orders for Latin letters to some extent.
Few-step distilled diffusion students cut text-to-image inference from ~50 to 1-8 network evaluations, but the quality gap is usually summarised by a single FID/CLIP scalar that cannot say which axis of the conditioning response changed, nor whether a behaviour comes from the architecture, the distillation objective, or simply from being a diffusion model. We replace the scalar with a decomposable probe that injects controlled perturbations along three layers (prompt encoder, denoiser input, denoiser output) under three modes (mean, variance, scale) and six strengths, reporting a bootstrap-median Bures W2^2 selectivity ratio on Inception features. Under a single matched estimator across 23 models — five teachers and 18 distilled students spanning five backbone families (SDXL, SD1.5, SD3.5, PixArt-alpha, FLUX), three architecture classes (UNet, DiT, MMDiT), and five distillation paradigms — the three layers read three empirically separable factors: the prompt layer is a universal prompt-mean response (a sanity channel, not a discriminator), the latent layer reads the prediction type, and the score layer reads the distillation objective. Our main result: within this sweep, the latent layer is a near-binary detector of rectified-flow backbones. Its ratio exceeds 1 across a sustained low-to-mid band only for rectified-flow models (SD3.5, FLUX); no epsilon-prediction model qualifies. A matched epsilon-prediction control (PixArt-alpha) rules out wide-T5 conditioning, and the fingerprint survives adversarial (ADD) distillation as both teacher and student. Two secondary score-layer findings hold under narrower scopes: a canonical 4-step ADD-vs-rest contrast on the UNet families with a non-ADD baseline, and a CI-separated trajectory-rollout early-strength score spike on both UNet and DiT. All ratios are CI-citable under one estimator; we release the per-cell tables and the estimator.
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Few-step distilled diffusion students cut text-to-image inference from ~50 to 1-8 network evaluations, but the quality gap is usually summarised by a single FID/CLIP scalar that cannot say which axis of the conditioning response changed, nor whether a behaviour comes from the architecture, the distillation objective, or simply from being a diffusion model. We replace the scalar with a decomposable probe that injects controlled perturbations along three layers (prompt encoder, denoiser input, denoiser output) under three modes (mean, variance, scale) and six strengths, reporting a bootstrap-median Bures W2^2 selectivity ratio on Inception features. Under a single matched estimator across 23 models — five teachers and 18 distilled students spanning five backbone families (SDXL, SD1.5, SD3.5, PixArt-alpha, FLUX), three architecture classes (UNet, DiT, MMDiT), and five distillation paradigms — the three layers read three empirically separable factors: the prompt layer is a universal prompt-mean response (a sanity channel, not a discriminator), the latent layer reads the prediction type, and the score layer reads the distillation objective. Our main result: within this sweep, the latent layer is a near-binary detector of rectified-flow backbones. Its ratio exceeds 1 across a sustained low-to-mid band only for rectified-flow models (SD3.5, FLUX); no epsilon-prediction model qualifies. A matched epsilon-prediction control (PixArt-alpha) rules out wide-T5 conditioning, and the fingerprint survives adversarial (ADD) distillation as both teacher and student. Two secondary score-layer findings hold under narrower scopes: a canonical 4-step ADD-vs-rest contrast on the UNet families with a non-ADD baseline, and a CI-separated trajectory-rollout early-strength score spike on both UNet and DiT. All ratios are CI-citable under one estimator; we release the per-cell tables and the estimator.
作者Marcus Häggbom, Viktor Nilsson, Pierre Nyquist, Joakim andén
Recent advances in generative modeling have enabled the efficient computation of Schrödinger bridges (SB) in high-dimensional settings by leveraging partially simulation-free training methods inspired by flow matching. However, these have not covered SBs with reflecting dynamics, a useful model choice with built-in guarantees that generated samples stay in the data domain. Existing alternatives for reflected SBs instead rely on more complex training based on forward--backward SDE theory, requiring expensive higher-order derivatives and sampling entire paths during training. In this article, we introduce a partially simulation-free framework that allows reflected SBs to be trained similarly to flow matching, using a new sampling method and regression target. We demonstrate our results by coupling pairs of well-known high-dimensional image datasets. Using reflected dynamics incurs negligible additional wall-clock time during both training and inference while maintaining or slightly improving generative performance.
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Recent advances in generative modeling have enabled the efficient computation of Schrödinger bridges (SB) in high-dimensional settings by leveraging partially simulation-free training methods inspired by flow matching. However, these have not covered SBs with reflecting dynamics, a useful model choice with built-in guarantees that generated samples stay in the data domain. Existing alternatives for reflected SBs instead rely on more complex training based on forward--backward SDE theory, requiring expensive higher-order derivatives and sampling entire paths during training. In this article, we introduce a partially simulation-free framework that allows reflected SBs to be trained similarly to flow matching, using a new sampling method and regression target. We demonstrate our results by coupling pairs of well-known high-dimensional image datasets. Using reflected dynamics incurs negligible additional wall-clock time during both training and inference while maintaining or slightly improving generative performance.
We propose Perceptual Flow Matching (PFM), a simple yet effective framework for few-step generation in flow-matching models. Rather than performing velocity regression in the conventional VAE latent space, PFM supervises flow matching in a perceptual feature space using pretrained perceptual models. This simple change substantially improves the few-step generation capability of flow-matching models, reducing the number of sampling steps from 35-50 to 4-8 while preserving generation quality. Unlike existing acceleration and distillation approaches, PFM requires neither teacher models nor auxiliary score networks and can be integrated into standard flow-matching training pipelines with minimal modifications. Extensive experiments on image generation, video generation, and image editing tasks demonstrate that PFM consistently produces high-quality results while producing fewer artifacts than existing distillation-based methods. We further show that perceptual supervision shifts the regression minimizer from mean-seeking to mode-seeking, biasing predictions toward on-manifold modes that remain accurate under coarse few-step integration. Our results reveal that standard flow-matching training can naturally yield high-quality few-step generators when supervised in an appropriate representation space. We hope this insight inspires future research into representation-aware objectives for efficient generative modeling.
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We propose Perceptual Flow Matching (PFM), a simple yet effective framework for few-step generation in flow-matching models. Rather than performing velocity regression in the conventional VAE latent space, PFM supervises flow matching in a perceptual feature space using pretrained perceptual models. This simple change substantially improves the few-step generation capability of flow-matching models, reducing the number of sampling steps from 35-50 to 4-8 while preserving generation quality. Unlike existing acceleration and distillation approaches, PFM requires neither teacher models nor auxiliary score networks and can be integrated into standard flow-matching training pipelines with minimal modifications. Extensive experiments on image generation, video generation, and image editing tasks demonstrate that PFM consistently produces high-quality results while producing fewer artifacts than existing distillation-based methods. We further show that perceptual supervision shifts the regression minimizer from mean-seeking to mode-seeking, biasing predictions toward on-manifold modes that remain accurate under coarse few-step integration. Our results reveal that standard flow-matching training can naturally yield high-quality few-step generators when supervised in an appropriate representation space. We hope this insight inspires future research into representation-aware objectives for efficient generative modeling.
作者Long Vu, Tan Ngo, Animesh Karnewar, Amir Habibian, Binh-Son Hua, Hung Bui, Minh Hoai Nguyen, Phong Nguyen-Ha
Modern image-and-text-to-video diffusion models can synthesize highly realistic videos by iteratively denoising an initial Gaussian noise tensor conditioned on reference image and text inputs. However, existing approaches still lack precise and unified controllability over both object motion and camera motion within a single generation process. We present UniCaMo, a unified framework that enables simultaneous control of object trajectories and camera viewpoints by directly constructing the input noise of the diffusion model. Specifically, UniCaMo builds a shared 3D-grounded motion-consistent noise space across latent video frames. Sparse 3D point tracks are used to warp the Gaussian noise of the reference frame along desired object trajectories, while a virtual spherical noise representation provides globally consistent noise values for newly revealed scene regions under camera motion. By combining local track-guided noise warping with global sphere-based noise sampling, UniCaMo maintains geometric and temporal consistency under both object movement and viewpoint changes. Because UniCaMo modifies only the input noise, it requires no auxiliary adapters, control branches, or architectural changes to the underlying video diffusion model. With lightweight LoRA fine-tuning on large pretrained video diffusion models, including Wan 2.1 (14B), UniCaMo achieves state-of-the-art results in both video quality and motion controllability on standard controllable video generation benchmarks.
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Modern image-and-text-to-video diffusion models can synthesize highly realistic videos by iteratively denoising an initial Gaussian noise tensor conditioned on reference image and text inputs. However, existing approaches still lack precise and unified controllability over both object motion and camera motion within a single generation process. We present UniCaMo, a unified framework that enables simultaneous control of object trajectories and camera viewpoints by directly constructing the input noise of the diffusion model. Specifically, UniCaMo builds a shared 3D-grounded motion-consistent noise space across latent video frames. Sparse 3D point tracks are used to warp the Gaussian noise of the reference frame along desired object trajectories, while a virtual spherical noise representation provides globally consistent noise values for newly revealed scene regions under camera motion. By combining local track-guided noise warping with global sphere-based noise sampling, UniCaMo maintains geometric and temporal consistency under both object movement and viewpoint changes. Because UniCaMo modifies only the input noise, it requires no auxiliary adapters, control branches, or architectural changes to the underlying video diffusion model. With lightweight LoRA fine-tuning on large pretrained video diffusion models, including Wan 2.1 (14B), UniCaMo achieves state-of-the-art results in both video quality and motion controllability on standard controllable video generation benchmarks.
作者Juan Diego Rodriguez, Jocelyn Zhang, Katrin Erk, Greg Durrett
Large language models are inconsistent: varying prompts or including unrelated information can lead to unexpected changes in model outputs. The generator-validator (G-V) gap is one manifestation of this phenomenon, where LLMs generate responses that they then deem as invalid if re-queried to validate them. In this work, we introduce a new formulation of G-V consistency that involves a principled correction for utterance frequency. Specifically, generators often assign low likelihood to valid strings simply because those strings are a priori unlikely, which makes naive notions of G-V consistency unworkable. We show that under a natural model of rational agents answering questions with multiple answers, consistency of the validator with a frequency-corrected generator score emerges naturally. Our method, \FCPAname (\FCPA), is a training objective implementing frequency-corrected G-V consistency for real-world LLMs. Our experimental results show that training with \FCPA{} substantially improves both G-V consistency and generator performance over prior methods, with gains of up to $+27$pp in Pearson correlation on IFEval and HumanEval, while preserving validator quality across all evaluated tasks.
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Large language models are inconsistent: varying prompts or including unrelated information can lead to unexpected changes in model outputs. The generator-validator (G-V) gap is one manifestation of this phenomenon, where LLMs generate responses that they then deem as invalid if re-queried to validate them. In this work, we introduce a new formulation of G-V consistency that involves a principled correction for utterance frequency. Specifically, generators often assign low likelihood to valid strings simply because those strings are a priori unlikely, which makes naive notions of G-V consistency unworkable. We show that under a natural model of rational agents answering questions with multiple answers, consistency of the validator with a frequency-corrected generator score emerges naturally. Our method, \FCPAname (\FCPA), is a training objective implementing frequency-corrected G-V consistency for real-world LLMs. Our experimental results show that training with \FCPA{} substantially improves both G-V consistency and generator performance over prior methods, with gains of up to $+27$pp in Pearson correlation on IFEval and HumanEval, while preserving validator quality across all evaluated tasks.
While diffusion models have revolutionized image synthesis, their application to real-world inverse problems is often hampered by the need for massive datasets and the difficulty of imposing strict physical constraints. In this work, we introduce SE-UNet (Singular Equivariant UNet), a framework designed to solve ill-posed imaging tasks without extensive pre-training. By treating generation as an optimization problem constrained by geometric equivariance ($D_4$ group) and singular value gating, SE-UNet effectively standardizes the solution space. We demonstrate that these strong inductive biases allow for state-of-the-art zero-shot inpainting results (80% missing pixels) on CIFAR-10. Our method surpasses Deep Image Prior (DIP) baselines by over 4 dB in PSNR and exhibits a characteristic "singular snap" convergence — rapidly locking into the signal manifold. SE-UNet thus offers a data-efficient pathway for constrained generation, aligning with the ReALM-GEN goal of bridging theoretical priors with practical deployment.
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While diffusion models have revolutionized image synthesis, their application to real-world inverse problems is often hampered by the need for massive datasets and the difficulty of imposing strict physical constraints. In this work, we introduce SE-UNet (Singular Equivariant UNet), a framework designed to solve ill-posed imaging tasks without extensive pre-training. By treating generation as an optimization problem constrained by geometric equivariance ($D_4$ group) and singular value gating, SE-UNet effectively standardizes the solution space. We demonstrate that these strong inductive biases allow for state-of-the-art zero-shot inpainting results (80% missing pixels) on CIFAR-10. Our method surpasses Deep Image Prior (DIP) baselines by over 4 dB in PSNR and exhibits a characteristic "singular snap" convergence — rapidly locking into the signal manifold. SE-UNet thus offers a data-efficient pathway for constrained generation, aligning with the ReALM-GEN goal of bridging theoretical priors with practical deployment.
Diffusion-based generative models have transformed visual content synthesis, yet they remain vulnerable to unauthorized usage and lack reliable attribution methods. Existing watermarking techniques often treat latent tensors as static spatial feature maps or depend on pixel-domain modification, and most do not explicitly leverage the internal frequency structure of the latent space for dual-band redundant embedding, leaving them susceptible to the stochastic nature of diffusion and regeneration attacks. We introduce BiSLW, a trainable bi-spectral latent watermarking framework that jointly embeds aligned identity signals across complementary spectral bands of the decoded diffusion latent using learned encoders and decoders, going beyond fixed-pattern frequency approaches. We leverage the inherent frequency structure of diffusion latents to design a dual-band watermarking framework. Low-frequency components encode global semantics, while high-frequency components capture fine texture. We exploit this structure to embed watermarks across complementary spectral bands. The watermark is independently injected into both bands via learned encoders and recombined before decoding, ensuring it becomes intrinsic to the generative trajectory. Dual spectral decoders recover the watermark from each band, while a cross-band consistency constraint enforces alignment between semantic and textural embeddings. Experiments show that BiSLW achieves a strong balance between perceptual fidelity and robustness, improving PSNR by over 3 dB compared to prior latent diffusion watermarking methods while preserving near-perfect bit accuracy under aggressive regeneration and common distortions, all with negligible computational overhead.
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Diffusion-based generative models have transformed visual content synthesis, yet they remain vulnerable to unauthorized usage and lack reliable attribution methods. Existing watermarking techniques often treat latent tensors as static spatial feature maps or depend on pixel-domain modification, and most do not explicitly leverage the internal frequency structure of the latent space for dual-band redundant embedding, leaving them susceptible to the stochastic nature of diffusion and regeneration attacks. We introduce BiSLW, a trainable bi-spectral latent watermarking framework that jointly embeds aligned identity signals across complementary spectral bands of the decoded diffusion latent using learned encoders and decoders, going beyond fixed-pattern frequency approaches. We leverage the inherent frequency structure of diffusion latents to design a dual-band watermarking framework. Low-frequency components encode global semantics, while high-frequency components capture fine texture. We exploit this structure to embed watermarks across complementary spectral bands. The watermark is independently injected into both bands via learned encoders and recombined before decoding, ensuring it becomes intrinsic to the generative trajectory. Dual spectral decoders recover the watermark from each band, while a cross-band consistency constraint enforces alignment between semantic and textural embeddings. Experiments show that BiSLW achieves a strong balance between perceptual fidelity and robustness, improving PSNR by over 3 dB compared to prior latent diffusion watermarking methods while preserving near-perfect bit accuracy under aggressive regeneration and common distortions, all with negligible computational overhead.
作者Tyler Farghly, Benjamin Dupuis, Alain Durmus, Umut Simsekli
Benign overfitting and double descent have come to shape our understanding of generalization in deep learning, establishing that overfitting is not only compatible with good generalization but can actively benefit it. Diffusion models share much of the machinery of standard deep learning, so it is natural to assume that they also exhibit these properties. In this work, we show that this assumption is largely incorrect. We first establish fundamental impossibility results showing that, unless the sample size grows exponentially with the data dimension, overfitting and good generalization cannot occur simultaneously. Consequently, the population loss follows a classical U-shaped curve in model complexity rather than exhibiting double descent. Analyzing a simplified setting, we identify a key difference between regression and score matching: regression benefits from an alignment between the target and the empirical covariance; score matching admits no such alignment, leaving overfitting irreparably harmful. We further identify implicit regularization stemming from time-smoothness of the score and early stopping during training as mechanisms that prevent such overfitting and verify our findings with high-dimensional image generation experiments. Our results reveal that generalization in diffusion models is governed by mechanisms distinct from those of traditional regression, motivating the development of new theory.
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Benign overfitting and double descent have come to shape our understanding of generalization in deep learning, establishing that overfitting is not only compatible with good generalization but can actively benefit it. Diffusion models share much of the machinery of standard deep learning, so it is natural to assume that they also exhibit these properties. In this work, we show that this assumption is largely incorrect. We first establish fundamental impossibility results showing that, unless the sample size grows exponentially with the data dimension, overfitting and good generalization cannot occur simultaneously. Consequently, the population loss follows a classical U-shaped curve in model complexity rather than exhibiting double descent. Analyzing a simplified setting, we identify a key difference between regression and score matching: regression benefits from an alignment between the target and the empirical covariance; score matching admits no such alignment, leaving overfitting irreparably harmful. We further identify implicit regularization stemming from time-smoothness of the score and early stopping during training as mechanisms that prevent such overfitting and verify our findings with high-dimensional image generation experiments. Our results reveal that generalization in diffusion models is governed by mechanisms distinct from those of traditional regression, motivating the development of new theory.
High-throughput long-context generation is one of the central challenges for large language models. Generation is typically memory-bandwidth-bound rather than compute-bound: each decoding step must stream the accumulated key/value (KV) cache from memory, so bandwidth demand grows with context length while only one token is emitted. Two parallel approaches have therefore emerged: reducing memory access with efficient attention variants and linear-time mixers such as Mamba, or increasing parallel computation by generating blocks of tokens at once. However, technical challenges arise when combining these two ideas. Earlier hybrid diffusion models such as DiffuMamba use bidirectional Mamba mixing, including a reverse-direction scan relative to causal generation. This reverse scan needs to scan the entire sequence, so its states are not prefix-only and cannot be precisely reused as a cache even when diffusion is performed block by block. We propose a BDLM Mamba--attention hybrid that addresses this challenge by restricting the reverse Mamba scan to the active denoising block, which enables exact caching across blocks. In an 87M-parameter DCLM sweep, BDLM Mamba-H achieves the best C4-en validation perplexity compared to BDLM attention and full-sequence baselines. At 350M parameters, it remains competitive with BDLM attention. For long-context inference, BDLM Mamba-H reaches 19.7x the throughput of full-sequence DiffuMamba-H at 65K tokens and 3.7x the throughput of BDLM attention at 262K, showing that Mamba hybrids are a potential long-context diffusion architecture.
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High-throughput long-context generation is one of the central challenges for large language models. Generation is typically memory-bandwidth-bound rather than compute-bound: each decoding step must stream the accumulated key/value (KV) cache from memory, so bandwidth demand grows with context length while only one token is emitted. Two parallel approaches have therefore emerged: reducing memory access with efficient attention variants and linear-time mixers such as Mamba, or increasing parallel computation by generating blocks of tokens at once. However, technical challenges arise when combining these two ideas. Earlier hybrid diffusion models such as DiffuMamba use bidirectional Mamba mixing, including a reverse-direction scan relative to causal generation. This reverse scan needs to scan the entire sequence, so its states are not prefix-only and cannot be precisely reused as a cache even when diffusion is performed block by block. We propose a BDLM Mamba--attention hybrid that addresses this challenge by restricting the reverse Mamba scan to the active denoising block, which enables exact caching across blocks. In an 87M-parameter DCLM sweep, BDLM Mamba-H achieves the best C4-en validation perplexity compared to BDLM attention and full-sequence baselines. At 350M parameters, it remains competitive with BDLM attention. For long-context inference, BDLM Mamba-H reaches 19.7x the throughput of full-sequence DiffuMamba-H at 65K tokens and 3.7x the throughput of BDLM attention at 262K, showing that Mamba hybrids are a potential long-context diffusion architecture.
作者Weiyi Xue, Fan Lu, Chi Zhang, Tianhang Wang, Sanqing Qu, Zehan Zheng, Boyuan Zheng, Junqiao Zhao, Guang Chen
3D Gaussian Splatting has demonstrated remarkable potential in novel view synthesis. In contrast to small-scale scenes, large-scale scenes inevitably contain sparsely observed regions with excessively sparse initial points. In this case, supervising Gaussians initialized from low-frequency sparse points with high-frequency images often induces uncontrolled densification and redundant primitives, degrading both efficiency and quality. Intuitively, this issue can be mitigated with scheduling strategies, which can be categorized into two paradigms: modulating target signal frequency via densification and modulating sampling frequency via image resolution. However, previous scheduling strategies are primarily hardcoded, failing to perceive the convergence behavior of scene frequency. To address this, we reframe the scene reconstruction problem from the perspective of signal structure recovery and propose SIG, a novel scheduler that synchronizes image supervision with Gaussian frequencies. Specifically, we derive the average sampling frequency and bandwidth of 3D representations, and then regulate the training image resolution and the Gaussian densification process based on scene frequency convergence. Furthermore, we introduce Sphere-Constrained Gaussians, which leverage the spatial prior of initialized point clouds to control Gaussian optimization. Our framework enables frequency-consistent, geometry-aware, and floater-free training, achieving state-of-the-art performance by a substantial margin in both efficiency and rendering quality in large-scale scenes. The code is available at: https://github.com/weiyixue999/Signal_Structure_Aware_Gaussian
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3D Gaussian Splatting has demonstrated remarkable potential in novel view synthesis. In contrast to small-scale scenes, large-scale scenes inevitably contain sparsely observed regions with excessively sparse initial points. In this case, supervising Gaussians initialized from low-frequency sparse points with high-frequency images often induces uncontrolled densification and redundant primitives, degrading both efficiency and quality. Intuitively, this issue can be mitigated with scheduling strategies, which can be categorized into two paradigms: modulating target signal frequency via densification and modulating sampling frequency via image resolution. However, previous scheduling strategies are primarily hardcoded, failing to perceive the convergence behavior of scene frequency. To address this, we reframe the scene reconstruction problem from the perspective of signal structure recovery and propose SIG, a novel scheduler that synchronizes image supervision with Gaussian frequencies. Specifically, we derive the average sampling frequency and bandwidth of 3D representations, and then regulate the training image resolution and the Gaussian densification process based on scene frequency convergence. Furthermore, we introduce Sphere-Constrained Gaussians, which leverage the spatial prior of initialized point clouds to control Gaussian optimization. Our framework enables frequency-consistent, geometry-aware, and floater-free training, achieving state-of-the-art performance by a substantial margin in both efficiency and rendering quality in large-scale scenes. The code is available at: https://github.com/weiyixue999/Signal_Structure_Aware_Gaussian
In this paper, we consider the nonsmooth nonconvex decentralized optimization problem, where inter-agent communication is compressed. We propose a general framework that unifies various decentralized stochastic subgradient-type methods with unbiased compression and contractive compression with error compensation. By relating the consensus-error iterates and the averaged iterates to the trajectories of continuous-time differential inclusions, we establish global convergence for all methods encompassed by our framework when the objective functions are nonsmooth and lack Clarke regularity. Based on our framework, we further develop several compression-based methods, including decentralized stochastic subgradient methods utilizing sign-based regularization and gradient-tracking momentum. Preliminary numerical experiments empirically support our theoretical results and highlight the communication-accuracy trade-off of the newly developed methods.
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In this paper, we consider the nonsmooth nonconvex decentralized optimization problem, where inter-agent communication is compressed. We propose a general framework that unifies various decentralized stochastic subgradient-type methods with unbiased compression and contractive compression with error compensation. By relating the consensus-error iterates and the averaged iterates to the trajectories of continuous-time differential inclusions, we establish global convergence for all methods encompassed by our framework when the objective functions are nonsmooth and lack Clarke regularity. Based on our framework, we further develop several compression-based methods, including decentralized stochastic subgradient methods utilizing sign-based regularization and gradient-tracking momentum. Preliminary numerical experiments empirically support our theoretical results and highlight the communication-accuracy trade-off of the newly developed methods.
Text-conditioned human interaction generation must capture both long-range temporal causality within each individual and tightly coupled coordination between partners. Existing interaction diffusion models typically denoise full sequences using bidirectional attention, which obscures causality and hinders streaming and long-horizon generation. Autoregressive alternatives enforce causality but often suffer from temporal drift, leading to coordination degradation and unstable interaction dynamics over time. We propose InterCMDM, a block-causal latent diffusion framework for autoregressive two-person interaction generation. InterCMDM introduces a Dual-Stream Causal Diffusion Transformer that maintains separate causal streams for each person while modeling inter-person dependencies via unified dual-stream attention with multi-task attention masks. These masks unify interaction modeling within a single attention mechanism and support diverse coordination behaviors, including simultaneous actions, reactive responses, leader-follower dynamics, and independent motion. By training a single model across these mask configurations as a form of data augmentation, InterCMDM enables controllable interaction generation by simply selecting the desired attention mask at inference time. Finally, a block-wise diffusion objective enables stable latent rollout over long sequences without repeated decode-encode cycles. InterCMDM achieves state-of-the-art performance on InterHuman and Inter-X, improving text-motion alignment, realism, and long-horizon continuity.
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Text-conditioned human interaction generation must capture both long-range temporal causality within each individual and tightly coupled coordination between partners. Existing interaction diffusion models typically denoise full sequences using bidirectional attention, which obscures causality and hinders streaming and long-horizon generation. Autoregressive alternatives enforce causality but often suffer from temporal drift, leading to coordination degradation and unstable interaction dynamics over time. We propose InterCMDM, a block-causal latent diffusion framework for autoregressive two-person interaction generation. InterCMDM introduces a Dual-Stream Causal Diffusion Transformer that maintains separate causal streams for each person while modeling inter-person dependencies via unified dual-stream attention with multi-task attention masks. These masks unify interaction modeling within a single attention mechanism and support diverse coordination behaviors, including simultaneous actions, reactive responses, leader-follower dynamics, and independent motion. By training a single model across these mask configurations as a form of data augmentation, InterCMDM enables controllable interaction generation by simply selecting the desired attention mask at inference time. Finally, a block-wise diffusion objective enables stable latent rollout over long sequences without repeated decode-encode cycles. InterCMDM achieves state-of-the-art performance on InterHuman and Inter-X, improving text-motion alignment, realism, and long-horizon continuity.
Recent advances in 3D content generation from text or images have achieved impressive results, yet view inconsistency from 2D generators and the scarcity of high-quality 3D data remain significant bottlenecks. Existing solutions typically adapt large-scale pre-trained text-to-image latent diffusion models to generate 3D Gaussian Splats (3DGS). However, these approaches often rely on training complex cascade pipelines that are computationally expensive and scalability-limited. Most critically, the quality of generated 3D assets is inherently constrained by each component capacity and compressed latent space, leading to decoding artifacts and accumulated errors. To address these limitations, we propose PixGS, a single-stage pipeline for direct high-quality 3DGS generation, which leverages recent advances in pixel-space diffusion to bypass lossy latent compression while still benefiting from the vast 2D generative priors. By directly denoising 3D Gaussian attributes at each timestep, our method enables precise, splat-level regularization of both appearance and geometry. Furthermore, we introduce a comprehensive supervision strategy that incorporates surface normals, depth, and high-frequency structural information, which is often overlooked in prior works. Experiments demonstrate that PixGS outperforms current state-of-the-art methods while maintaining a fast inference speed (1s on a single A100 GPU), offering a robust and efficient alternative to multi-stage generation pipelines.
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Recent advances in 3D content generation from text or images have achieved impressive results, yet view inconsistency from 2D generators and the scarcity of high-quality 3D data remain significant bottlenecks. Existing solutions typically adapt large-scale pre-trained text-to-image latent diffusion models to generate 3D Gaussian Splats (3DGS). However, these approaches often rely on training complex cascade pipelines that are computationally expensive and scalability-limited. Most critically, the quality of generated 3D assets is inherently constrained by each component capacity and compressed latent space, leading to decoding artifacts and accumulated errors. To address these limitations, we propose PixGS, a single-stage pipeline for direct high-quality 3DGS generation, which leverages recent advances in pixel-space diffusion to bypass lossy latent compression while still benefiting from the vast 2D generative priors. By directly denoising 3D Gaussian attributes at each timestep, our method enables precise, splat-level regularization of both appearance and geometry. Furthermore, we introduce a comprehensive supervision strategy that incorporates surface normals, depth, and high-frequency structural information, which is often overlooked in prior works. Experiments demonstrate that PixGS outperforms current state-of-the-art methods while maintaining a fast inference speed (1s on a single A100 GPU), offering a robust and efficient alternative to multi-stage generation pipelines.
作者Kyobin Choo, Youngmin Kim, Hyunkyung Han, Geunrip Park, Chanyoung Kim, Sunyoung Jung, Seong Jae Hwang
Video diffusion transformers (DiTs) generate high-fidelity and temporally coherent videos, yet motion control remains implicit, primarily relying on text prompts. As a result, achieving desired motion often requires extensive prompt engineering and repeated resampling. While fine-tuning models with additional spatial prompts (e.g., bounding boxes or point trajectories) enables explicit control, it demands substantial data curation and computation, and may compromise the generative capabilities of pretrained models. Consequently, training-free motion control using such spatial prompts has been explored in U-Net-based video diffusion models, but remains largely unexplored for DiTs. We introduce QWERTY, a training-free framework that enables flexible motion control in pretrained image-to-video DiTs via user-defined object warping and optical flow. We carefully manipulate the 3D full attention of DiTs by warping the frame-invariant semantic subspace of queries. We find that the noise predicted by the query-warped DiT naturally guides the diffusion trajectory toward the desired motion, and further show that leveraging this noise as self-guidance for latent optimization improves control stability and visual quality. Experiments show that QWERTY achieves the most effective motion control among existing training-free approaches on a recent image-to-video DiT, with performance comparable to fine-tuning-based methods.
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Video diffusion transformers (DiTs) generate high-fidelity and temporally coherent videos, yet motion control remains implicit, primarily relying on text prompts. As a result, achieving desired motion often requires extensive prompt engineering and repeated resampling. While fine-tuning models with additional spatial prompts (e.g., bounding boxes or point trajectories) enables explicit control, it demands substantial data curation and computation, and may compromise the generative capabilities of pretrained models. Consequently, training-free motion control using such spatial prompts has been explored in U-Net-based video diffusion models, but remains largely unexplored for DiTs. We introduce QWERTY, a training-free framework that enables flexible motion control in pretrained image-to-video DiTs via user-defined object warping and optical flow. We carefully manipulate the 3D full attention of DiTs by warping the frame-invariant semantic subspace of queries. We find that the noise predicted by the query-warped DiT naturally guides the diffusion trajectory toward the desired motion, and further show that leveraging this noise as self-guidance for latent optimization improves control stability and visual quality. Experiments show that QWERTY achieves the most effective motion control among existing training-free approaches on a recent image-to-video DiT, with performance comparable to fine-tuning-based methods.
The rise of customized diffusion models has fueled a boom in personalized visual content creation, but it also introduces serious risks of malicious misuse, thereby posing threats to personal privacy. Image aesthetics are strongly correlated with human perception of image quality. Motivated by this observation, we address facial privacy protection from a novel aesthetic perspective by degrading the generation quality of maliciously customized models, thus reducing facial identity leakage. Specifically, we propose a Hierarchical Anti-Aesthetics (HAA) framework that exploits aesthetic cues at multiple perceptual levels. HAA consists of two key branches: (1) Global Anti-Aesthetics, which degrades overall aesthetics and generation quality by constructing a global anti-aesthetic reward mechanism and a corresponding loss; and (2) Local Anti-Aesthetics, which disrupts facial identity by using a local anti-aesthetic reward mechanism and loss to guide adversarial perturbations toward facial regions. By integrating both branches, HAA achieves anti-aesthetic degradation from a global to a local level during customized generation. Extensive experiments show that HAA outperforms existing methods in identity removal, providing an effective tool for protecting facial privacy.
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The rise of customized diffusion models has fueled a boom in personalized visual content creation, but it also introduces serious risks of malicious misuse, thereby posing threats to personal privacy. Image aesthetics are strongly correlated with human perception of image quality. Motivated by this observation, we address facial privacy protection from a novel aesthetic perspective by degrading the generation quality of maliciously customized models, thus reducing facial identity leakage. Specifically, we propose a Hierarchical Anti-Aesthetics (HAA) framework that exploits aesthetic cues at multiple perceptual levels. HAA consists of two key branches: (1) Global Anti-Aesthetics, which degrades overall aesthetics and generation quality by constructing a global anti-aesthetic reward mechanism and a corresponding loss; and (2) Local Anti-Aesthetics, which disrupts facial identity by using a local anti-aesthetic reward mechanism and loss to guide adversarial perturbations toward facial regions. By integrating both branches, HAA achieves anti-aesthetic degradation from a global to a local level during customized generation. Extensive experiments show that HAA outperforms existing methods in identity removal, providing an effective tool for protecting facial privacy.