生成模型理论与方法

Despite remarkable progress in text-guided image editing, generative models frequently fail to preserve visual object consistency, defined as the preservation of a subject's key attributes throughout the editing process. We address this limitation through three contributions. First, we introduce ABO-Edit, a dataset specifically designed to study object consistency, comprising over 12,000 triplets of source images, editing prompts, and high-quality target images rendered from artist-designed 3D assets, with multi-view coverage and human-verified quality control. Second, we uncover an overlooked property of image-editing rectified flow models: the conditioning embedding space, not directly supervised during training, encodes a prediction of the final generated image even at high noise levels. Third, exploiting this finding, we propose FlowMirror, a parameter-free auxiliary loss that supervises this conditioning embedding space. Without architectural changes, our method improves generation quality across several metrics over baselines.

Vision Transformers (ViTs) achieve strong accuracy but incur high inference latency. Semi-structured N:M sparsity can reduce arithmetic cost, yet its theoretical savings often fail to translate into proportional end-to-end speedups on modern GPUs. This mismatch arises because deployment latency depends not only on arithmetic reduction but also on execution regularity and hardware scheduling under sparsity. Achieving practical acceleration, therefore, requires coordinated design across sparse execution and sparsity configuration. To this end, we propose a hardware-software co-design framework for N:M sparse ViT inference. On the hardware side, we design MD-SpMM, an N:M sparse CUDA kernel that reorganizes sparse GEMM into micro-dense, Tensor-Core-aligned dataflow and uses inference-aware adaptive parallelism to sustain utilization. On the software side, we perform layer-wise sparsity search under explicit end-to-end latency budgets using a three-stage heuristic search with constraint relaxation to avoid premature convergence and enable deployment-aware sparsity allocation. Experiments on multiple ViT/Swin models and GPU platforms show that the framework achieves over 2.2x latency speedup while maintaining comparable accuracy and delivering superior accuracy under the same latency constraint. The source code is publicly available at https://github.com/liuganhuo/realizable-nm-sparse-transformer.

Accurately modeling the dynamics of planetary parachute and entry vehicle systems is critical for Entry, Descent, and Landing events such as vehicle separation and sensor activation. These dynamics are difficult to capture with traditional system-identification methods as parachute motion is highly nonlinear, the governing equations are not fully known, and relevant test data are scarce and expensive to acquire. In this work, we sidestep these challenges by leveraging a physics-aware generative modeling approach that learns parachute dynamics directly from data. The proposed method, Symplectic Parachute Generative Adversarial Network (SPar-GAN), adapts a Hamiltonian generative architecture to the parachute setting by conditioning on canopy design and freestream velocity, while enforcing conservation of energy through symplectic integration. We apply SPar-GAN to subscale parachute tests conducted at the National Full-Scale Aerodynamics Complex and show that it reproduces qualitatively accurate pitch-yaw dynamics of different parachute configurations while recovering a compact two-degree-of-freedom phase-space consistent with canopy axisymmetry. These results suggest that physics-constrained generative models can characterize parachute dynamics across operating conditions and may help reduce the volume of physical testing required to assess performance.

Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen. However, before any operator is applied, the grid has already determined how modeling capacity is allocated across space, resolution, and spectral bandwidth. We argue that this hidden design choice should itself be learnable, leading to a question different from standard operator learning: can a surrogate learn where resolution should exist before predicting field evolution? We formulate adaptive discretization as a physics-constrained conditional generation problem over valid mesh displacements. The success of diffusion models in PDE field prediction suggests their potential for learning adaptive discretizations under similar structured constraints. This leads to a two-stage diffusion framework: Stage 1 learns an r-adaptive displacement mesh conditioned on the observed dynamics, while Stage 2 predicts the solution evolution from the mesh-informed representation. The mesh generator is regularized by physics-aware proxy channels, geometric validity constraints, and local spectral concentration so that adaptation remains physically interpretable and numerically legal. Across five PDE regimes, the results show that diffusion-based learned discretization is competitive with adaptive-mesh and reduced-order baselines, with particularly strong gains in regimes where fixed or handcrafted allocation is insufficient. The main conclusion is not that there exists a universal optimal mesh rule, but that discretization should be learned in a regime-dependent manner: different spatial and spectral structures favor different allocation behaviors. This reframes adaptive meshing for neural PDE solvers from a solver-specific heuristic into a generative representation-learning problem.

Machine learning models for system diagnostics rely on kernel execution traces to capture fine-grained system behavior, but collecting production traces in industrial systems is costly due to runtime overhead, storage demands, and privacy constraints. We present TraceSynth, a diffusion-based framework for generating synthetic kernel traces that augment limited real data for downstream ML tasks. TraceSynth models traces as multi-channel sequences (event types, timestamps, CPU affinity, thread identifiers, and process metadata) using a Transformer-based denoising diffusion process with constraint-guided repair to enforce system invariants. Across six benchmarks, results show strong workload dependence. For deterministic, compute-heavy workloads (scimark2), synthetic augmentation achieves 87.2% F1-Macro at context length L=4096, only 2.6 percentage points below real-only baselines. Context length is the dominant quality factor, with L=4096 yielding a +104% relative improvement over L=256, while constraint-guided repair improves synthetic data quality by up to 4.3%. Ablation studies show that lightweight 2-channel models retain 97-99% of the performance of full 6-channel models at roughly half the computational cost. TraceSynth supports cost-effective augmentation of kernel execution traces in production observability pipelines and helps identify when synthetic data can substitute for limited real traces.

In rectified-flow-based generative models, the neural network can be trained to predict two different targets, such as the instantaneous velocity or the data endpoint, to perform denoising. Although prior work shows that these parameterizations lead to different empirical behaviors, the mechanisms underlying their respective advantages remain to be underexplored, and how to combine them effectively is still unclear. In this work, we analyze how learning errors from different parameterizations affect the generation performance. We show that predicting the data endpoint has a clear training signal that stabilizes training, whereas predicting the velocity maintains stable sampling dynamics near the data manifold. Motivated by these insights, we propose Self-Consistent Flow (SC-Flow), a new method that unifies the benefits of both parameterizations. By employing a lightweight consistency loss, SC-Flow jointly trains a single network to predict both the local velocity and the data endpoint, and the consistency between the two predictions improves the model's performance. The method requires no major architectural changes and adds minimal computational overhead. Extensive experiments on image generation tasks demonstrate that SC-Flow substantially stabilizes optimization and improves the straightness of generation paths, leading to significant gains in generation quality over standard rectified-flow baselines.

Diffusion models have become the central backbone for modern image, video, and audio generation, but their efficient service remains a challenge. Unlike autoregressive decoding, diffusion inference repeatedly updates high-dimensional spatial or temporal latents over many denoising steps. This all-region execution pattern makes generation latency high and limits serving throughput. Existing multi-GPU parallelization methods can reduce per-step computation, but often introduce substantial activation exchange overhead, causing communication to offset or even outweigh the benefits of parallel execution. This paper presents FlashDiff, a diffusion serving system that improves inference efficiency through adaptive regional execution and scheduling. FlashDiff is based on the observation that diffusion refinement is not uniform across latent regions or denoising steps: different regions often stabilize at different rates, while neighboring steps exhibit strong temporal correlation. FlashDiff leverages these properties to selectively execute only regions that require further refinement and to reallocate the resulting compute slack across concurrent serving requests. FlashDiff consists of three mechanisms. First, it decomposes the latent representation into coherent execution regions using early-stage attention signals, preserving semantic structure while exposing fine-grained parallelism. Second, it uses a lightweight runtime controller to estimate region activity and bypass low-impact updates when further refinement is unlikely to affect output quality. Third, it applies an affinity-aware online scheduler that co-locates dependent regions, balances residual load across GPUs, and reuses reclaimed compute capacity to improve serving efficiency. Across real-world image, video, and audio workloads, FlashDiff reduces end-to-end serving latency by 30-97% and improves throughput by 1.2-2.2x.

Subgroup analysis is important in practice because real-world data typically come from heterogeneous populations, where meaningful patterns can differ substantially across subpopulations. Correctly identifying these subgroups can improve prediction accuracy, prevent biased or misleading conclusions, and support more effective, targeted decision-making. While most existing subgroup analysis methods are developed for complete data, in this paper we propose a novel and robust approach for censored data under heterogeneous accelerated failure time (AFT) models. Specifically, we combine inverse probability weighting, M-estimation, and concave pairwise fusion penalization to simultaneously identify subgroups and estimate covariate effects for heterogeneous censored data, without requiring prior knowledge of individual subgroup memberships. We further develop an efficient RISA-ADMM algorithm to implement the method and establish its convergence. Furthermore, we derive the theoretical properties of the proposed estimators under mild regularity conditions. Extensive simulations and an application to the German credit dataset demonstrate the robustness and effectiveness of our approach.

We study the problem of efficient online proportional sampling from a high-dimensional domain under a $σ$-smoothed adversary, where the sampling distribution is induced by a dynamically evolving weight function defined over a sequence of piecewise-structured partitions. This setting captures a broad range of applications, including principal-agent games (e.g., pricing and contract design), and algorithm configuration and parameter tuning. The central challenge is maintaining an efficient data structure as the induced partition grows increasingly complex over time — naively, the number of subregions can grow as $O(t^d)$ by round $t$ in $d$ dimensions. We design a data structure that supports efficient updates and proportional sampling while avoiding the cost of explicitly maintaining this exponential growth, where the discontinuities are structured from axis-parallel hyperplanes. Under a $σ$-smoothed adaptive adversary, we prove a tight $O(\sqrt{σT})$ bound on the depth of our data structure, and an $O(\log T)$ bound under a random-order adversary — to our knowledge, the first such results for this class of problems. We apply this framework to online learning with piecewise-structured rewards, obtaining efficient no-regret algorithms under both full-information and bandit feedback, with provable sublinear regret guarantees.

We study the coupled objective J_K^WOR = E_{S ~ PL-WOR_K}[max_{i in S} R_i]: the expected maximum reward of a size-K Plackett-Luce draw without replacement, the law of Gumbel-Top-K / Stochastic Beam Search decoding. This estimand differs from the conventional i.i.d. objective J_K^iid = E[max_{i<=K} R_i] targeted by existing sample-reuse Max@K estimators, and reusing their i.i.d. weights under the coupled sampler is provably biased (a closed-form three-item instance gives E[g_iid] = (4/5) grad J_K^WOR exactly; pass@K under the coupled sampler is the binary-reward special case). Generic joint-score REINFORCE is already unbiased for J_K^WOR; what it lacks is sample reuse. Our contribution is to instantiate standard rank-conditioned Horvitz-Thompson estimation for the J_K^WOR subset total: from one Gumbel-Top-n pool (n>K) and its observed priority threshold we build an estimator that reuses all C(n,K) embedded K-subsets, unbiased with an unbiased exact score-function surrogate gradient, plus a reward-sorted Max-specific dynamic program that collapses the C(n,K)-term subset sum (with K!-cost set probabilities) exactly to a one-dimensional integral. A fixed-Q quadrature evaluation costs O(n log n + nKQ) arithmetic and is numerically, not algebraically, exact; no epsilon-approximation rate is certified. Each nonzero degree-K Horvitz-Thompson term has finite second moment exactly when n >= 2K; under the same assumptions the full surrogate gradient has finite second moment whenever n >= 2K (sharpness there is open). At K=1 the construction recovers classical priority sampling. All quantities require only the values and differentiable computation graphs of the n+1 drawn items' probabilities, so finite structured sequence policies sampled by exact SBS are covered. A certified finite-Q quadrature bound and countably infinite support remain open. Validation code is included as ancillary files.

Recent advances in text-to-image (T2I) generation have led to models capable of producing highly realistic images. Yet, reliably evaluating their outputs remains challenging, especially at scale. Existing automatic evaluators, often relying on a static prompt set, struggle to capture subtle failure modes such as partial prompt misalignment, compositional errors, or visually plausible but semantically incorrect generations. In this work, we introduce DynEval, a Dynamic Evaluation framework designed to jointly assess text-to-image alignment and image quality of T2I models. To support scalable training beyond limited human-annotated data, we construct two large datasets. First, we build GenDB, a collection of 500K prompt-image pairs generated from human-written prompts drawn from DiffusionDB using a tiered prompt-model generation strategy. Second, building upon GenDB, we construct DynEvalInstruct, a 250K instruction dataset comprising prompt-image-response triplets distilled from a structured evaluation pipeline that decomposes evaluation into text-image alignment and visual quality reasoning. Using this dataset, we perform full fine-tuning of a compact evaluator through a curriculum learning strategy to effectively distill the superior evaluation capabilities of a larger teacher vision-language model, resulting in DynEval-2B and DynEval-4B. In extensive comparisons against existing evaluators across 11 benchmarks, our evaluator achieves a higher overall correlation with human judgments. Furthermore, it provides fine-grained analysis of the capabilities and failure modes of 36 T2I models across 42 subcategories and 9 semantic dimensions.

For close-contact human-robot interaction (HRI), trunk-like continuum manipulators provide a physical channel for diverse whole-body expression, but grounding open-vocabulary responses into such robots is difficult: end-effector motion underspecifies body shape, whereas direct whole-body commands are high-dimensional and hard to keep feasible. We propose a whole-body semantic-to-actuation grounding framework for elephant-inspired soft-trunk HRI based on lightweight flow matching. The framework converts responses from a multimodal large language model into bounded, morphology-aligned intent-intensity tuples, parameterizes tendon-actuation trajectories with compact Catmull-Rom spline controls, and uses a rectified-flow generator to sample feasible whole-body trunk motions. Experiments show that the proposed framework improves held-out grounding correctness from 25.0% to 77.2% over a raw-response dense-regression baseline. Compared with a denoising-diffusion baseline, it improves correctness from 71.9% to 77.2% and reduces inference time from 7.86 ms to 4.87 ms while preserving motion diversity. A 100-participant physical HRI study further shows that adding the generated soft-trunk motion channel increases the positive overall-satisfaction rating from 46% to 82% over the audiovisual-only baseline.

Imitation learning enables robots to acquire manipulation skills from demonstrations by mapping observations to actions. Existing approaches predict either short-horizon continuous action sequences or discrete keyposes. However, continuous prediction methods suffer from compounding errors due to short prediction horizons and struggle with multi-modal action distributions, whereas keypose-based methods necessitate an external planner, constraining real-time applicability. To address these challenges, we introduce SegDiff, a closed-loop visuomotor policy that integrates the strengths of both paradigms. SegDiff decomposes demonstrations into motion segments between keyposes and learns to predict the continuous trajectory from the current state to the next keypose, enabling long-horizon prediction with real-time refinement. Furthermore, we leverage the capability of diffusion models and DDIM inversion to propose a Dynamic Temporal Ensembling mechanism, which allows the policy to efficiently respond to dynamic environments and mitigate discontinuities caused by inconsistent multi-modal sampling. SegDiff demonstrates significant performance gains over existing approaches across various simulated and real-world scenarios, indicating its strong ability to reason over extended temporal dependencies while maintaining real-time adaptability and control stability.

Conditional diffusion models can generate anatomically plausible medical ultrasound (US) images, but anatomical plausibility alone does not ensure realistic B-mode appearance. Most US pipelines adapt standard generative architectures and condition them on anatomical masks, or use guidance mechanisms that reinforce the same anatomical signal. However, B-mode US images are shaped by acquisition-dependent properties such as speckle texture, tissue contrast, and attenuation. Using a frozen US foundation model, we show that standard conditional diffusion baselines remain separated from real images in representation space. In this work, we propose Feature-Space Candidate Guidance (FSCG), a training-free sampling strategy to reduce this gap. At sampling time, FSCG applies local k-NN feature correction and selects the best of multiple stochastic candidates according to their feature-space energy. In this way, the mask defines the anatomy, while FSCG steers samples toward the real US domain. Across three different datasets, FSCG reduces average FID64 by 56%, FID192 by 57%, and nearest-neighbour feature distance by 47% over standard conditional diffusion sampling, outperforming alternative inference-time guidance baselines. The results suggest that domain-aware feature representations can reveal and reduce realism gaps in medical diffusion synthesis without retraining the generator. Our code is available at https://github.com/marinadominguez/FSCG.

Sampling from multimodal distributions is a longstanding challenge for classical local Markov chain Monte Carlo (MCMC) methods. A popular remedy is to introduce a sequence of intermediate distributions that interpolate between the target and a simpler reference. The classical choice, tempering, raises the density to a power, but distorts the relative weights of asymmetric modes and can lead to poor mixing. We instead propose interpolating along the diffusion path, the marginals of a noising diffusion process that carries the target toward a Gaussian. This path preserves the relative weights of the modes and enjoys favorable mixing properties, which we make precise through a spectral-gap analysis of the corresponding ideal transition kernel. Sampling along the path requires its intermediate scores, which can be estimated from the unnormalized target through variational approaches, yielding only an approximate sampler. To remove the resulting bias, we introduce the Metropolis-adjusted diffusion path (MAD-Path) sampler, which corrects the diffusion-path proposal in an augmented path space and leaves the target invariant regardless of the accuracy of the learned score or the discretization error. We further quantify how these two errors affect the acceptance probability, providing guidance for practical tuning. Experiments on a range of Bayesian posteriors show that MAD-Path improves global exploration and mode-weight estimation relative to tempering-based MCMC methods and unadjusted diffusion samplers.

Accurate monocular 4D hand reconstruction remains challenging. Per-frame discriminative regressors lack temporal context and often produce jittery predictions. Temporal models improve consistency by aggregating information across frames, but they are typically deterministic regressors, making them vulnerable to ambiguous observations caused by occlusion and motion blur. Generative modeling offers a natural alternative by learning a prior over plausible hand motion sequences, enabling coherent hand-state recovery when visual evidence is incomplete or unreliable. Motivated by this observation, we present HandFlow, a fully generative flow-matching framework for temporally coherent 3D hand pose and shape estimation from monocular video. Given visual and skeletal observations, HandFlow denoises an entire temporal window of MANO parameters through a single ODE integration. To support this, we use a Flux-style dual-stream transformer that attends across the full sequence to capture long-range dependencies without autoregressive decoding, and a confidence-aware continuous masking mechanism that blends observed features with learnable mask tokens to handle noisy or missing observations. Experiments on DexYCB and HOT3D show that HandFlow achieves state-of-the-art performance, with particularly large gains in world-space accuracy and temporal smoothness. It reduces world-space pose error by over 30% compared with the strongest baseline and achieves the lowest acceleration error among all evaluated methods, while remaining competitive in per-frame pose accuracy. Moreover, on a single GPU HandFlow reconstructs a 150-frame sequence at 47 fps, about 12x faster than the fastest prior video-based method, with reconstruction itself accounting for only a small fraction of the end-to-end latency.

Low-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models, where the inherent phase-space contraction leads to the numerical extinction (``wash-out'') of weak but diagnostically critical lesion signals. To overcome this geometric limitation, we propose FlowPET, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergence-free vector field by construction, theoretically immunizing weak signals against probability mass collapse. To steer this conservative flow, we introduce conjugate boundary conditions based on the Range-Null space decomposition of the PET operator; this strictly enforces data consistency in the range space while confining stochastic uncertainty injection to the unobserved null space. We train the model via symplectic flow matching and perform inference using a symplectic leapfrog integrator. Extensive experiments on BrainWeb, clinical pediatric, and UDPET datasets demonstrate that FlowPET not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM and PSNR but, more crucially, exhibits superior recovery of low-contrast lesions. The results confirm that imposing Hamiltonian structural constraints offers a robust geometric safeguard for medical inverse problems in high-noise regimes.

While diffusion models achieve state-of-the-art image quality for text-to-image (T2I) generation, recent work has demonstrated that they suffer from sample diversity collapse. In this work, we investigate whether autoregressive (AR) image generation models can push the Pareto frontier between image quality and sample diversity. With recent advances in quality and efficiency, AR models have emerged as a viable alternative to diffusion-based image generation. Beyond enabling new use cases such as interleaved image-text generation, their sequential generation process makes them compatible with a wide range of token-based decoding strategies originally developed to improve diversity in text generation. Motivated by the potential of a better diversity-quality tradeoff in the AR paradigm, we present the first systematic study of sample diversity in AR image generation models. We show that two key properties of AR image generation, persistently high token-level entropy and substantial redundancy in visual token spaces, limit the effectiveness of existing token-level decoding methods for diversity enhancement. We therefore propose $p$-less cluster, a new decoding strategy that performs entropy-based truncation sampling at cluster level rather than at token level. We evaluate our approach and baseline decoding methods across four autoregressive T2I models and two datasets using a comprehensive suite of metrics spanning image quality, prompt alignment, and diversity. Our results show that $p$-less cluster unlocks the greatest diversity across most evaluated autoregressive T2I models and datasets while maintaining image quality and prompt alignment.

We introduce Self-Similar Generative Estimation (SS-GEN), a method for simulating multivariate tail events and estimating rare-event probabilities in both heavy and light-tailed settings. SS-GEN exploits asymptotic tail structure to decompose the tail distribution into an explicit radial component and a nonparametric angular component, reducing tail learning to a compact-domain problem that can be handled by off-the-shelf deep generative models. The resulting sampler generates representative extreme scenarios and supports probability estimation far beyond the observed data. Under mild nonparametric tail assumptions, we show that the SS-GEN density is asymptotically exact in the tail, with vanishing uniform relative error for regularly varying distributions and vanishing uniform log-relative error for Weibull-type distributions. Unlike existing approaches that rely on specialized architectures or parametric tail specifications, SS-GEN leverages asymptotic tail structure to enable standard generative models to generate representative extreme samples and estimate rare-event probabilities beyond the observed data.

Many geometric statistics and manifold learning pipelines routinely produce observations — such as tangent vectors or local frames — whose natural home is a varying family of fibers attached to different points of a base manifold, rather than a single shared vector space. Forming empirical averages requires transporting these observations to a common reference fiber, thereby introducing curvature- and holonomy-driven effects that are absent from classical concentration theory. We develop a non-asymptotic concentration theory for such transported empirical means, deriving finite-sample, dimension-free Hoeffding- and Bernstein-type bounds via sharp Hilbert-space inequalities. When shortest paths to the reference point are non-unique, transport becomes path-dependent and introduces a deterministic holonomy bias; we isolate and quantify this bias through bundle curvature and loop geometry, with sharp closed-form formulas for the tangent bundle of a round sphere. The resulting bias-variance decomposition separates the stochastic fluctuation decaying at the classical $n^{-1/2}$ rate in sample size $n$, from a curvature-driven error floor that no amount of additional data can eliminate; minimax lower bounds confirm both terms are unavoidable. We further establish a robust median-of-means estimator achieving optimal rates under heavy tails and the central limit theorem in the reference fiber. Controlled experiments on the sphere validate all theoretical predictions.

Deep generative models are increasingly used as simulators for downstream decision-making under data scarcity, but in risk-sensitive applications their usefulness depends on rare adverse scenarios rather than typical samples. Standard generative objectives prioritize bulk distributional fidelity, leaving low-probability tails vulnerable to localized optimization noise and making tail-dependent functionals unstable under finite simulation budgets. We introduce Diachronic Sample Integration (DSI), a test-time inference framework that ensembles generated samples across checkpoints from a stochastic training trajectory. DSI targets a checkpoint-mixture distribution that averages checkpoint-specific tail fluctuations rather than relying on a single brittle endpoint. We formalize this mechanism through a finite-budget bias-variance theory. Empirically, across multivariate synthetic processes and high-frequency trading data, DSI substantially reduces tail-estimation error compared to single-checkpoint baselines under fixed simulation budgets, outperforming standard diffusion and state-of-the-art tail-aware baselines without modifying the generative objective.

We introduce Sticky Jump Diffusions (SJDs), continuous-time Markov processes on $\mathbb R^d$ whose discrete anchors are token embeddings. In forward time, anchors release their mass at a hazard rate and the released mass diffuses in the continuous ambient space; time reversal couples a score-driven SDE with a sticky jump kernel whose rate and destination are fixed by flux balance with the forward law. We estimate the score and the per-anchor reverse hazards from a single denoising classifier via Denoising Hazard Matching, the hazard analogue of denoising score matching, with simulation-free cross-entropy training. SJD recovers masked diffusion, continuous diffusion, and hybrid diffusion as limits. Its reversal explains features that each family treats as given: the mask of masked diffusion carries no evidence about the source token because the unsticking kernel of every anchor collapses to the same absorbing point; the terminal projection of continuous diffusion is required due to the absence of atoms in its forward marginal, without which flux balance yields no reverse jumps; and the update rules of hybrid diffusion (commit rate, destination, and drift) all follow from flux balance rather than from separate design. Beyond these limits, the unsticking kernel becomes a design space: a cross-position blending corrupts each position toward a blend of its neighbors' clean values or embeddings, turning dependency structure such as spatial locality or a constraint graph into an inductive bias of the corruption itself, and improves over the identity-kernel hybrid on CIFAR-10, Text8, and Sudoku.

Diffusion models faithfully reproduce their training distribution, but also inherit its imbalances and leave rare or under-represented modes hard to reach. A natural inference-time remedy is to sample from the high-temperature target $p^{(γ)}_0(x) \propto p_0(x)^γ$ for $0 < γ< 1$, which flattens dominant modes and lifts rare ones. However, naive score scaling while correctly reweighting modes also inflates the per-mode variance, breaking the reverse diffusion process and degrading sample quality. We introduce variance-corrective time shifting, a training-free fix that queries the network at a shifted timestep and scales the resulting score by $γ$, canceling the variance inflation while preserving the mode reweighting. The correction turns simple temperature sampling into a practical diversity knob for pretrained diffusion and flow-matching backbones with no retraining, and we demonstrate consistent gains at minimal cost to sample quality and condition fidelity across DiT, Stable Diffusion and Motion Diffusion models. We further show that the timing of the temperature intervention enables coarse-to-fine control: high-noise stages drive compositional diversity across modes, while low-noise stages drive local appearance variation under a fixed composition.

Generative models often represent signals as dense grids of amplitudes, blurring sharp transients that are crucial for the correctness of physical signals. We introduce Singularity Space, a generative framework that represents signals through complex-plane singularities, rooted in the classical pole-residue representation of meromorphic functions. We learn a latent space of physically constrained, per-signal singularity configurations to solve an inverse problem from degraded or partial observations. The framework has three key properties: interpretability, in which each generated singularity configuration corresponds to a set of physical parameters; structural stability, which mitigates Gibbs artifacts at discontinuities; and resolution-free output reconstruction on arbitrary grids without retraining or interpolation. Our framework employs a transformer-based diffusion model that directly predicts samples at complex-plane singularity coordinates, subject to geometric constraints during sampling. As a controlled test case for sharp-feature recovery, we evaluate our framework on 1D Burgers shocks, where each shock is represented by 32 predicted singularities (an $8\times$ reduction versus a 1024-point grid signal). Our framework preserves signal structure ($\text{TV ratio} \approx 1$) under unseen test-time observation noise, achieves a $4.2\times$ lower reconstruction error in zero-shot sub-resolution generalization than a grid-based baseline, and recovers physical parameters to $10^{-4}$ absolute error in-distribution. These results suggest that singularity-based representations may provide a practical foundation for other transient-dominated signals such as speech and biomedical signals, with potential extension to higher-dimensional domains.

Activation steering offers a lightweight alternative to fine-tuning for controlling large language models at inference time. While many existing methods implicitly optimize a log-density-ratio objective between desired and undesired activation distributions, they do so heuristically rather than deriving it from a principled optimization problem. Moreover, these methods produce query-independent steering directions that can degrade performance on both in-distribution and out-of-distribution (OOD) inputs. We introduce \textsc{Cobras} (Conditional Optimal Bridge for Riemannian Activation Steering), which addresses both limitations by casting activation steering as a Schrödinger Bridge on the residual-stream hypersphere. This formulation yields, to our knowledge, the first principled derivation of the log-density-ratio steering objective from a well-posed optimization problem. Solving the bridge via entropic optimal transport and extracting the probability flow ODE recovers the widely used density-ratio gradient as a special case when the Sinkhorn potentials are uniform. Crucially, the Schrödinger potentials are evaluated at the current activation, making the resulting steering direction inherently query-adaptive. Empirically, across four models and three alignment axes (helpfulness, truthfulness, and detoxification), \textsc{Cobras} consistently outperforms prior activation steering baselines while avoiding the OOD degradation commonly observed in existing methods. The code can be found at https://github.com/arshandalili/cobras.

Computed tomography (CT) is a critical imaging modality for clinical diagnosis, but reducing radiation dose inevitably introduces severe noise and structured artifacts that degrade image quality. Existing deep learning-based low-dose CT (LDCT) reconstruction methods are typically optimized for fixed dose levels or specific anatomical regions, limiting their robustness and generalization in realistic clinical settings. We propose GenDiff, a generalizable diffusion-based framework for LDCT reconstruction that jointly models continuous radiation dose and anatomical information within a unified reconstruction network. The proposed framework integrates a Dose-Anatomy Encoder to learn acquisition-aware embeddings, a dose- and anatomy-conditioned cold diffusion backbone for iterative refinement, a physics-consistency update to enforce fidelity to the CT forward model, and a Structural Prior Refinement Module (SPRM) that preserves anatomical structures while suppressing dose-dependent artifacts. Extensive experiments on multi-anatomy clinical datasets, including unseen ultra-low-dose conditions as well as out-of-distribution phantom and animal datasets, demonstrate that GenDiff consistently outperforms state-of-the-art convolutional neural network and diffusion-based reconstruction methods. The proposed approach achieves superior reconstruction quality while maintaining strong robustness across different dose levels, anatomical regions, and acquisition domains, making it a promising solution for practical low-dose CT imaging.

While autoregressive models optimize the exact data likelihood via the chain rule, diffusion models are typically trained with denoising objectives. We develop conservation laws based on generalized extrinsic information transfer (GEXIT) functions for a broad class of memoryless noise processes, showing that the data--model cross-entropy (CE) can be characterized exactly as an integral of local information-theoretic derivatives along the noise path. This yields a unified characterization of the likelihood for discrete and continuous diffusion, with the Gaussian case reducing to the well-known mutual information--minimum mean-square error (I-MMSE) relationship. An immediate implication is a locality property: one can compute the information-theoretic derivatives using only the marginal posteriors along the noise path. As a result, training reduces to learning the marginal posteriors by minimizing the negative log-likelihood. While the conservation law implies that the entropy does not depend on the noise path, finite-capacity denoisers approximate the posteriors with varying accuracy across noise types, leading to differences in performance. We validate these predictions on synthetic Markov sources and standard benchmarks, including text8 and CIFAR-10.

Text-to-image diffusion models exhibit unprecedented generative capability and contain rich intermediate representations that can be useful for discriminative vision tasks. Motivated by this observation, we study a focused question: how can the denoising dynamics of a pretrained diffusion model be adapted to support discriminative representation learning while preserving its generative behavior under parameter-efficient updates? We present D$^3$CL as an investigation of this question. Our key observation is that noisy latents at different diffusion timesteps can be interpreted as stochastic views of the same underlying image, enabling a contrastive objective to be coupled with the standard denoising reconstruction loss. This formulation provides a simple way to probe the interaction between generative denoising and discriminative representation learning without training from scratch. To keep the adaptation lightweight, we apply LoRA updates to a pretrained Stable Diffusion backbone while freezing the original model parameters. D$^3$CL provides strong empirical evidence that reconstruction and noise-level contrastive objectives can be complementary: on ImageNet-1K, it obtains 80.1% linear-probing accuracy and an FID of 5.56 for $256 \times 256$ unconditional generation. Additional ablations on the design space suggest that the usefulness of diffusion features depends on where and how denoising states are sampled. These results establish D$^3$CL as a parameter-efficient adaptation framework for pretrained diffusion models, showing that noise-level contrastive learning can structure denoising representations for discriminative tasks while maintaining generative performance.

Three-dimensional (3D) molecule generation has been dominated by diffusion models, which achieve strong generation quality but typically require the molecular size to be specified a priori. Recent autoregressive approaches have substantially narrowed the performance gap while naturally supporting variable-length generation and conditioning on partial molecular context. However, balancing unconditional and context-conditioned generation remains challenging. We introduce KRONOS, a latent autoregressive diffusion framework that generates molecules in the latent space of a pre-trained autoencoder, jointly modeling molecular graph topology and geometry, while retaining the flexibility of autoregressive generation. We further introduce a mixed training strategy inspired by Fill-in-the Middle (FIM) paradigm, enabling both unconditional and fragment-conditioned molecular generation within a single left-to-right autoregressive model. Experiments on QM9 and GEOM-Drugs demonstrate that KRONOS achieves leading unconditional generation performance among autoregressive methods, while remaining competitive with diffusion models. Moreover, fragment-conditioned generation is achieved with negligible impact on unconditional generation performance, demonstrating that both generation paradigms can be supported within a single architecture.

The ability to generate variable-length proteins is crucial in protein design, where the optimal length is often unknown and tightly coupled to designability. Current diffusion- and flow-based generative models typically require the protein length to be specified before sampling, limiting their flexibility in exploring the feasible design space. To address this limitation, we introduce Generalized Poisson Flow (GPFlow), a variable-length generative framework that learns the rate function of an inhomogeneous generalized Poisson process by minimizing its negative log-likelihood. We establish population-level guarantees for recovering the joint multimodal distribution and derive an upper bound on the KL divergence between the data and generated distributions. We comprehensively evaluate GPFlow across structure and sequence design, motif scaffolding, and peptide co-design, spanning Euclidean, categorical, and Riemannian modalities to fully validate its variable-length generation quality. In unconditional design, GPFlow improves structural designability and achieves the best distributional fitness for sequence design compared to their corresponding fixed-length baselines, while perfectly recovering the length distribution. In conditional motif scaffolding, GPFlow ranks first on 10 of 16 structure-based design tasks with significantly more unique successes and also achieves more passed tasks in sequence-based design. In peptide co-design, GPFlow remains competitive even without access to a native-length oracle.