生成模型理论与方法

Diffusion models offer flexible motion generation, but translating this flexibility into feedback-responsive humanoid control remains challenging. Hierarchical systems steer motion through references that may exceed a separate tracker's capabilities, leaving recovery and physical execution largely to the tracker. Action-only diffusion generates actions directly but lacks an explicit future-state trajectory for test-time motion objectives. Joint state-action diffusion provides this representation, yet representative controllers often depend on privileged full-body states, and support for learned behavior selection and test-time motion steering remains fragmented. We present PredActor, a predictive action diffusion policy that brings these complementary steering capabilities into one directly executed policy using proprioceptive observations. Conditioned on proprioceptive history and optional task context, PredActor jointly generates executable actions and an internal future-state trajectory. Classifier-free guidance strengthens text-conditioned behavior, while classifier guidance steers predicted states toward test-time objectives. Only actions are executed, without a separate motion-reference tracker or externally estimated full-body states as policy inputs. In simulation, PredActor reaches 44 of 45 destination targets and achieves a text retrieval score of 0.539, compared with 0.424 for conditional action diffusion, with similar observed disturbance survival. To make this guided policy practical onboard, rolling denoising and computation-preserving runtime optimizations reduce the complete callback to 16.790 ms median and 19.383 ms p95 on a Jetson Orin NX, both below the 20 ms control period. We deploy PredActor on a Unitree G1; evaluations across simulation and physical hardware demonstrate text-conditioned motion, disturbance response, joystick control, and semantic interpolation.

This work studies prediction parameterization for stochastic generative dynamics in diffusion models. Existing velocity-based generative models provide the simplicity of learning a single transport field, but their standard formulation is deterministic, whereas stochastic extensions generally require additional score information or an intermediate velocity-to-score reconstruction. To retain single-field prediction while directly supporting stochastic reverse dynamics, this paper introduces Mean Velocity Matching (MVM). MVM constructs a Gaussian perturbation process for which the conditional expectation of a restoration-oriented velocity, $(x_0-x_t)/t$, directly forms the reverse-SDE drift. Consequently, a single learned field is sufficient to parameterize the stochastic reverse process without separately estimating or reconstructing the score. Because direct regression of this velocity becomes unbounded near $t=0$, MVM further introduces a $\sqrt{t}$-scaled parameterization that preserves the reverse dynamics while yielding a bounded training target. The same learned field also induces a deterministic probability-flow ODE, enabling stochastic and deterministic sampling to be studied within a unified formulation. Experiments with Transformer-based generative models achieve an FID of $\MVMImageNetThirtyTwoFID$ at \MVMImageNetThirtyTwoNFE\ NFE on ImageNet $32\times32$ and $\MVMImageNetTwoFiftySixFID$ at \MVMImageNetTwoFiftySixNFE\ NFE on ImageNet $256\times256$. Controlled SDE--ODE comparisons further show that the ODE performs better under very low NFE, whereas the stochastic reverse process achieves lower FID when sufficient function evaluations are available. These results demonstrate that MVM provides a direct single-field parameterization of stochastic reverse dynamics while maintaining competitive generation quality.

Although uniform diffusion language models (UDLMs) represent a promising diffusion paradigm, scaling them remains challenging. We identify the core obstacle as an over-uniform training objective and condition-target confusion during sampling. To address these, we propose Less Uniform Diffusion (LUDI), a novel UDLM framework. Specifically, we (i) introduce a less uniform loss that directs each reverse transition toward the clean token, and (ii) equip the model with per-token time embeddings that supply token-level corruption hints, enabling confidence-based few-step sampling. Experiments across scales show that LUDI yields cleaner supervision and improves few-step generation. We further continue-train a 7B autoregressive model into LUDI-7B, resulting in a UDLM capable of complex reasoning. It achieves a 3-token-per-step speedup over AR decoding and competitive performance compared with masked diffusion baselines, revealing that the full potential of UDLMs for complex generation remains to be unlocked.

Counterfactual image generation answers questions about how a subject would have looked under retrospective, hypothetical scenarios. Recent methods have improved perceptual quality, identity preservation and faithfulness to an underlying causal model, but their adoption in healthcare is limited by scarce annotated data, distribution shift between datasets, and mismatches between pretrained generative models and those required for counterfactual inference. We propose specialisation, a data and parameter-efficient framework for adapting pretrained, non-causal generative models into causal mechanisms under distribution shift. Based on this framework, we train a radiology counterfactual image generation model, called RadCF, using latent flow matching. We validate our approach on three chest X-ray datasets spanning different dataset shifts, data volumes, and counterfactual questions, associated with challenging, highly-localised interventions. Our results show that RadCF and specialisation improve counterfactual soundness over existing methods while being data and parameter efficient, and that the resulting counterfactuals can detect and mitigate shortcut learning in a downstream medical classifier. Code is available at https://github.com/GSK-AI/RadCF/.

Recent advances in pixel-space diffusion models have narrowed the image quality gap with latent-space diffusion, but still converge more slowly and lag behind in final image quality. We argue that a key reason is the lack of an explicit representation prior: unlike latent diffusion, which usually denoises in a compact and structured latent space, pixel diffusion needs to learn denoising-friendly representations and pixel generation simultaneously from raw RGB space. To address this problem, we propose PixelDiT2, an end-to-end pixel-space diffusion model designed to decouple representation learning from pixel generation without introducing an autoencoder or latent reconstruction bottleneck. We propose representation grounding that uses a frozen pretrained vision foundation model to provide explicit per-patch representation guidance throughout denoising, allowing the pixel diffusion transformer to focus more on pixel generation. On ImageNet-256x256, PixelDiT2 achieves an FID of 1.46 after 600 epochs; at 512x512 resolution, PixelDiT2 achieves an FID of 1.48 after 680 epochs. Project page: https://pixeldit.github.io/pixeldit2/

Recent advances in video generative models have enabled high-fidelity, temporally coherent video generation. However, these models often struggle to satisfy prompts requiring specialized knowledge, specific identities, physical consistency, or ordered events. In this paper, we present VideoGen-Agent, a multimodal agent trained through multitask agentic reinforcement learning to use external tools for video generation. The agent coordinates augmentation, generation, and verification tools through multi-turn interactions, using the prompt and intermediate observations to guide its decisions. We train a shared policy on a category-balanced dataset spanning six tasks. Supervised fine-tuning on teacher-generated trajectories establishes tool-use behavior, which is then refined through reinforcement learning. A category-aware hybrid reward evaluates tool-call validity, task-appropriate tool use, and generated video quality. We further introduce VABench, a held-out benchmark of 600 prompts covering procedural knowledge, single- and multi-entity identity preservation, physical consistency, scene composition, and multi-shot temporal structure. On VABench, VideoGen-Agent improves over its base text-to-video generator by 19.1 points, from 56.5 to 75.6. Upgrading the generation tools further raises the score to 86.1 without additional agent training. Human raters prefer the upgraded configuration over the strongest standalone baseline in 84.3% of comparisons. These results support learning tool use across video-generation tasks and show that the trained agent can benefit from subsequent advances in generation tools. Project page: https://andyca111.github.io/VideoGen_Agent/

Image morphing aims to produce a smooth and semantically consistent transition between two input images. Existing diffusion-based morphing methods either require expensive per-pair optimization or rely on implicit spatial alignment, which easily fails under large layout discrepancies. To address these limitations, we propose AlignMorph, a novel tuning-free diffusion framework guided by the principle of transport-then-denoise. We explicitly decouple geometric alignment from generative denoising to avoid structural entanglement. Our framework consists of two core components. (1) Global Semantic Transport, which achieves diffusion-compatible semantic alignment via entropic optimal transport and reliability-aware latent warping; and (2) Coordinate-Aligned Generation, which uses a symmetric bi-phase attention handoff to maintain consistent spatial coordinates throughout denoising. Without any tuning, AlignMorph effectively eliminates ghosting and achieves superior structural coherence and temporal smoothness on morphing benchmarks. Code is available at https://github.com/51xOne/Alignmorph.

Graph Retrieval-Augmented Generation (GraphRAG) has remarkably enhanced large language models on complex reasoning by leveraging structured entity topologies. However, existing frameworks heavily rely on standard autoregressive language models where the nature of inherent sequential generation severely hinders overall inference efficiency. Inspired by Diffusion Language Models (DLMs) that offer massive parallelism via continuous refine-in-parallel decoding, we aim to accelerate GraphRAG in the discrete space. However, it remains non-trivial for two challenges. First, partially denoised drafts are highly dynamic and uncertain, making dynamic graph grounding non-trivial. Second, raw denoising states are inherently noisy and unstable, making synchronous graph retrieval and multi-hop aggregation computationally prohibitive. To this end, we present LADDER, a novel framework that bridges diffusion language modeling with GraphRAG through graph-guided parallel decoding. Specifically, (i) we propose an event-driven self-clocking retrieval, inspired by our key insight that 88% of target entities emerge early in the partially denoised state, leading final commitment by an average of 5.7-9.6 steps. This mechanism dynamically triggers graph retrieval only when the set of graph-linkable entities expands, yielding an asynchronous self-clocking policy that bypasses learned gates or heuristic thresholds. (ii) An incomplete-query graph propagation module is designed to process the newly emerging entity queries using a specialized graph foundation model, continuously aggregating multi-hop evidence to sharpen parallel predictions and accelerate overall decoding convergence. Extensive experiments on three challenging multi-hop QA benchmarks show that LADDER raises average exact match from 39.6% to 45.2% while achieving a 4.1x latency reduction.

Sparse attention reduces the quadratic cost of global self-attention while retaining strong empirical performance, but how its restricted interactions shape the evolution of token representations remains theoretically underexplored. Modeling tokens as particles on the unit sphere, we introduce opinion leader dynamics, a framework that identifies two mechanisms through which token groups converge internally while maintaining distinct limiting directions. In the explicit model, fixed representatives induce a potential that attracts tokens toward distinct local maxima. In the implicit model, disconnected interaction groups evolve toward separate consensus directions. We formulate both models as reverse Wasserstein gradient flows and establish exponential convergence under suitable conditions. We further connect these theoretical predictions to token evolution in frontier sparse-attention LLMs that motivate our framework. Across four benchmarks, Kimi-K3, MiniMax-M3, and DeepSeek-V4-Flash consistently exhibit clearer cluster separation and higher clustering scores than the dense-attention model GLM-4.7-Flash in projected token representations. These observations support the relevance of the predicted multiple-group structure to trained frontier LLMs, while finite-particle simulations illustrate the theoretical convergence behavior. Together, our results connect restricted token interactions to distinct group-level attractors, providing a dynamical account of how sparse attention can support alignment within groups while preserving separation between them.

Ambisonics Upscaling (AU) aims to enhance the spatial resolution of sound fields by estimating high-order Ambisonics (HOA) components from low-order observations. While deep learning and model-based strategies have been considered for AU, both approaches exhibit significant performance degradation in realistic scenarios, where reverberant sound fields violate the directional sparsity inherent to discriminative mappings. In this work, we address AU as a generative task rather than a deterministic reconstruction, expanding generative modeling to specifically target the recovery of spatial information in reverberant speech. We investigate two dominant continuous-time generative paradigms, adapting both Score-based Generative Model and Flow Matching to these complex acoustic settings. We provide an extensive numerical study comparing our methods against state-of-the-art baselines in various acoustic scenarios. Additionally, we conduct subjective listening tests to evaluate the perceived quality and spatial accuracy of the proposed generative framework across various reverberant scenarios. The studies reveal that Flow Matching consistently outperforms both its discriminative counterparts and Diffusion-based paradigms in all reverberant settings.

Bayesian filtering provides a principled framework for online state estimation under uncertainty, yet its application to systems with high-dimensional states and complicated posterior distributions remains challenging. Recent generative models, such as flow matching, have shown potential in Bayesian filtering. However, they still rely on particle-based representations of the posterior, which lose the rich information of the full distribution, or tackle a trajectory-level inverse problem that conflicts with the recursive structure of Bayesian filtering. To address this, we propose a new perspective of directly encoding the evolving distribution into flow matching model weights, namely, the Belief Flow Filter (BFF). It is a generative filtering framework that updates model weights via gradient descent at test time to track the posterior evolution. Thereby, BFF bypasses the scalability issue of particle representations or the flexibility limitation of Gaussian assumptions in conventional filters. We theoretically justify that the BFF design is structurally aligned with Bayesian filtering, and its training objective targets the recursive filtering operator. BFF is empirically verified across 5 different physical systems, including ones with chaotic dynamics and highly sparse, non-linear observations. The results show that BFF attains the best score in 8 of 9 metric-benchmark cells across the three standard 1D and 2D PDE benchmarks, and similarly leads on the extreme single-moving-sensor setting and on a real-world-grounded tokamak plasma estimation task, demonstrating its potential to accurately approximate the Bayesian filtering operator in high-dimensional probability space.

This paper presents a probabilistic perspective on large language models (LLMs), developed with the aim of bringing together, in a single self-contained account, tools that are usually treated separately across the literature. LLMs are described through probability measures on the set of sequences of tokens, specified via their autoregressive conditional distributions. Training is formulated as a maximum-likelihood estimation problem, addressed by stochastic gradient methods, while text generation is viewed as the sequential simulation of the resulting stochastic process. The role of the asymmetry of the Kullback--Leibler divergence in text generation is examined in relation with characteristic phenomena such as hallucination and the distinction between statistical plausibility and truth. As a complementary illustration of the same viewpoint, we also discuss diffusion models, built around the score function, which cast generation not as sequential token prediction but as the simulation of a reverse-time stochastic process transforming noise into data both in discrete and continuous time.

Despite impressive visual quality, state-of-the-art video diffusion models often generate content that violates real-world physical laws. While existing solutions rely on external priors or specialized data, we investigate the root cause by exploring the internal mechanisms of these models. Specifically, we present the first interpretability study on the ''motion planning'' process of text-to-video diffusion models, revealing how motion trajectories form during early denoising stages. Building upon the ''first shape, then details'' finding, we combine cross-attention trajectory patterns with causal head contributions to identify a specific subset of attention heads driving motion planning. Further, our self-attention analysis shows that Rotary Position Embedding (RoPE) induces excessive spatial attention decay. This causes early candidate regions to prematurely lock into physically implausible positions, suppressing reasonable trajectories in adjacent frames and triggering generation failure modes. To address this fundamental flaw, we propose a lightweight architectural modification that scales the frequency of RoPE across different denoising steps. This strategy reduces excessive attention decay, helping the model explore better candidate regions to establish coherent physical motion. Finally, training-free and training-based experiments confirm the effectiveness of our approach in enhancing the physical commonsense of generated videos.

Generative models of neural activity could help characterize tissue dynamics, compare experimental conditions, and simulate population activity for applications ranging from disease and drug-response studies to closed-loop experimentation. Existing approaches, however, typically assume a fixed set of sorted neurons, whereas high-density microelectrode arrays produce extremely sparse, array-wide binary spike volumes in which the observed subset of electrodes varies across assays. We introduce a discrete generative model that represents this activity using a shared vocabulary of spatiotemporal motifs. A residual vector-quantized autoencoder learns the motif vocabulary, while a factorized masked transformer predicts where activity occurs and which motif appears at each active location. We evaluate the model on 31 assays spanning human brain organoids and acute ex vivo human hippocampal tissue. The learned motifs are broadly reused: assay identity explains only $9%$ of the entropy in motif use, and motif overlap across tissue types is comparable to overlap within them. When representation quality is evaluated independently of the generative prior, our approach achieves $5.2\times$ the voxel-level reconstruction average precision of a matched flat tokenizer. For masked completion and free generation, the full model achieves $1.4$--$2.6\times$ the site-level average precision of the matched generative baseline and outperforms it across all four families of generation metrics. These results establish a compact, reusable representation for array-wide spiking activity without learned assay-specific parameters, providing a scalable foundation for generative modeling across diverse neural preparations.

Diffusion models generate high-quality images, yet often violate the physical laws governing mirror reflections. Reflections often suffer from geometric aberrations, including positional offsets, directional misalignment, proportional imbalance, and structural distortion. These failures remain evident even in contemporary state-of-the-art generative systems. Existing methods itigate this problem through synthetic data scaling or auxiliary depth conditioning, yet their merely reliance on latent-space noise reconstruction losses as implicit supervision prevents direct enforcement of reflection-specific geometric and perceptual constraints. To bridge this gap, we present PhysReflect, a geometry and perception guided diffusion framework that decodes the predicted clean latent into pixel space at each training step and applies annealed supervision through two complementary differentiable objectives. The Geometric Loss enforces mirror-induced spatial consistency through sparse epipolar correspondence and dense boundary projection alignment, where a SAM2-based TwinTrack mechanism provides stable in-mirror localization for boundary-aware supervision. The Perceptual Loss preserves reflected appearance by combining Semantic Consistency Loss, which maintains reflected identity and appearance via DINOv2 features, and Lighting Consistency Loss, which regularizes depth, surface-normal, and illumination coherence under monocular geometry priors. Experiments on synthetic and real-world benchmarks show that PhysReflect outperforms prior mirror-reflection methods in geometric, perceptual, and physical-plausibility metrics, as well as qualitative visual results.

Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SDR) provides a principled approach to compress these dependencies, traditional SDR frameworks were not formulated for conditional generation. To bridge this gap, we propose Belted Engression, a unified and architecturally parameter-efficient framework for generative distributional regression. Our approach establishes an end-to-end compress-then-generate paradigm driven by sufficient representation learning, embedding a structural bottleneck into the generative architecture. Theoretically, we prove that the standard SDR condition is equivalent to a law-preserving generative factorization, which is achieved at the global optimum of the population Belted Engression objective. Furthermore, by uncovering a localized Bernstein-type control for the energy-score loss, we establish finite-sample convergence rates that are sharper than those of existing results. We also prove that this belted architecture is strictly smaller, operating with an asymptotically vanishing parameter count relative to the unstructured baseline. Extensive simulations and real-world applications demonstrate that Belted Engression achieves superior distributional prediction and SDR recovery with fewer trainable parameters.

Counterfactual tool evaluation must distinguish authority, historical support, and what a comparison actually estimates. We study these distinctions with eleven executable enterprise-inspired tools, exact-propensity logs, and real local Model Context Protocol transport. An initial 45-run synthetic study is retained, then challenged by 30 realized-return control runs and 15 experiments on 1,930 independently released Berkeley Function Calling Leaderboard (BFCL) tasks. Full-return direct regression reverses an initially favorable doubly robust (DR) evaluation result in the linear setting: mean absolute errors are 0.0139 for direct regression and 0.0272 for DR. Under a shifted environment, DR retains an advantage, with errors 0.0227 versus 0.0948. On function-name-group-disjoint BFCL-derived splits, direct and DR selectors obtain balanced accuracies of 81.85% and 79.83%. Two pinned local Qwen2.5 models are evaluated on the same 200 held-out tasks, exposing a strong failure to abstain under the fixed prompt. We further characterize policy differences under missing support: unsupported actions shared by two policies cancel, allowing point identification of an incremental change when neither absolute value is identifiable. A disagreement-preserving fallback achieves this property in all five support-gap runs, but conservative sampling bounds do not certify deployment improvement. The contribution is a falsifiable evaluation method and independent public evidence, not a new DR estimator, official BFCL leaderboard score, or production-agent safety claim.

Whitening a foundation-model embedding and using its squared norm as a training-free likelihood surrogate is motivated by the observation that whitened coordinates often appear approximately standard normal. We show that this observation follows from the projection central limit theorem and therefore does not imply a Gaussian joint distribution. Across multiple encoders and three training objectives, we find systematic over-dispersion of the whitened radius relative to the Gaussian reference, including against distributional clones with identical mean and covariance. We further show that the commonly reported agreement between empirical and theoretical norm statistics is an algebraic consequence of in-sample whitening and does not constitute evidence for Gaussianity. We identify the mechanism behind this behavior: whitening reverses the encoder's spectral hierarchy, shifting the contribution to the squared norm toward near-degenerate directions that encode predominantly noise. In these directions, the dominant variability is governed by a single input-dependent scale. We estimate this scale from two moments and use it to predict, without additional free parameters, the cross-dependence between disjoint spectral halves. These results indicate that the squared whitened norm is better interpreted as a Mahalanobis measure of semantic atypicality than as a log-likelihood. This interpretation explains both its practical effectiveness and its calibration failures: the statistic can rank and detect atypical samples consistently with nonparametric density estimates and across encoders trained with different objectives, while Gaussian tail thresholds can be inaccurate by orders of magnitude. etc.

Diffusion models and transformers have supplanted GANs for multivariate time series imputation, largely on grounds of GAN training instability. R3GAN (NeurIPS 2024) removes that instability via regularized relativistic losses with provable convergence, raising a natural question: do stable, modern GANs revive adversarial imputation? We adapt R3GAN to 1D temporal data with a coarse-to-fine refinement framework and a frequency-domain discriminator, and audit 14 saved configurations across 3 datasets. Because these are heterogeneous single runs, the evidence is descriptive rather than a matched causal ablation. We report a negative result. All five saved mean/zero-start configurations improve by 48.4-70.2%. Among eight eligible non-legacy linear-start configurations, the mean change is -0.7% (range -3.0% to +1.1%); a separate -21.9% legacy logging anomaly is retained for provenance but excluded from that aggregate. In a saved Weather comparison, standalone R3GAN-1D underperforms BRITS by 5.8x. Crucially, we argue the common explanation (that GANs optimize distributional rather than point-wise objectives) cannot be the whole story, since diffusion models also optimize distributional objectives yet achieve state-of-the-art imputation. Our saved reconstruction-weight sweep is consistent with the adversarial signal being inert or harmful, but cannot identify its causal contribution; a matched discriminator-removed ablation is the key next experiment. We frame the precise reason a learned discriminator fails to provide useful refinement gradients (where a learned diffusion denoiser succeeds) as an open problem, and offer practical guidance on when adversarial refinement is worthwhile.

Diffusion models have demonstrated strong power in generative modeling tasks across multiple domains, exhibiting a remarkable capability of learning complex distributions from samples. In this paper, we leverage such capability to design an efficient universal diffusion-based solver for parameterized black-box optimizations (BBO), where the optimizer has only black-box access to queries of the objective function at the learning stage, yet is able to reduce the additional computational cost at the inference stage for each BBO instance while also capturing the potential multi-modal landscape of non-convex objectives. To cast our formulation as a compatible generative modeling task, we introduce the notion of minimization policy as a new solution concept, which defines a sampling distribution over the solutions that should concentrate around the minimizer set for each BBO instance. We then propose Diffusion-based Iterative Minimization Policy Learning (D-IMPL), a practical generative-model-based solver for solving parameterized BBOs that employs diffusion models to learn a minimization policy, whose density is proportional to the exponential of the negated objective values, thereby amortizing the computational costs across different BBO instances. Furthermore, we demonstrate the performance of our D-IMPL algorithm by establishing a sample complexity guarantee showing that a $δ$-approximate minimization policy can be effectively learned within $O(\log(1/δ))$ iterations, and by extensive empirical evaluations over a range of constrained and unconstrained BBO tasks.

Forecasting a long horizon from only the first observations of a sequence is ill-posed: many trajectories are consistent with the same short history. We study this problem in oil and gas production forecasting, where forecasts made after roughly the first fifth of a well's producing life drive development and abandonment decisions, and where a usable forecast must describe a monotone decline. We present Physics-SIMS-TS, a conditional diffusion forecaster that combines negative guidance against synthetic artifacts, decline-curve constraints and an isotonic projection applied during sampling, spatial training augmentation, and an ensembled stochastic sampler yielding a full predictive distribution. Across three jurisdictions and more than 35,000 wells, under a shared-space, validation-frozen protocol, Physics-SIMS-TS is the most accurate diffusion forecaster in the comparison and is competitive with, but not superior to, ensembled transformer forecasters. Its forecasts are monotone by construction at a cost of at most 0.5% in mean squared error, and its trajectory ensemble yields calibrated intervals after one dispersion factor is fitted per jurisdiction. On six standard benchmarks a reversible-instance-normalization variant of the backbone is the leading diffusion baseline. We also quantify four protocol choices on which the measured ranking depends. Code and evaluation artifacts are released.

Gradient-guided diffusion samplers provide flexible priors for inverse problems and conditional generation, but strong guidance can move the sampling trajectory into regions where the learned score is poorly supported. Existing tangent-projection strategies limit first-order departure from an iso-density surface, yet discard potentially useful normal motion and overlook the second-order departure induced by tangent motion on a curved surface. We introduce curvature-adaptive tubular correction (CAT), a training-free plugin that regulates both effects within a shared, noise-dependent geometric budget. CAT decomposes the guidance gradient into normal and tangent components, charges normal displacement at first order and tangent displacement according to directional curvature, and obtains their jointly optimal magnitudes from a one-dimensional dual equation. Armijo backtracking calibrates the resulting finite step against the actual guidance objective, while matrix-free directional derivatives avoid constructing the full score Jacobian. We establish local guarantees for the tubular approximation, uniqueness of the correction, and sufficient objective decrease. Across seven inverse problems on FFHQ and ImageNet, CAT improves the evaluated pixel- and latent-space host samplers, with particularly consistent gains in perceptual metrics. It also improves black hole reconstruction on InverseBench and yields the lowest FID among the compared methods at every tested classifier-free guidance scale, while maintaining stable saturation and contrast. These results support curvature-aware tubular control as a reusable mechanism for stabilizing diffusion guidance.

Multimodal large reasoning models (MLRMs) have demonstrated remarkable capabilities in complex visual understanding. However, this very power introduces a critical yet underexplored privacy threat: adversaries can exploit MLRMs to precisely infer users' geographic locations from casually shared photographs, by performing structured reasoning over subtle visual cues such as architectural styles, vegetation, and lighting conditions. In this work, we present a systematic study of MLRM-driven geolocation privacy leakage. We first reveal that refusal-based safeguards are critically insufficient, as carefully crafted jailbreak prompts can raise model response rates to 100%. We further identify that existing defenses, which inject imperceptible perturbations into shared images, suffer from structural limitations intrinsic to their pixel-space optimization, resulting in degraded black-box transferability and pronounced visual artifacts. Motivated by these findings, we propose a diffusion-based framework that provides targeted, proactive defense against geolocation privacy leakage. By injecting perturbations into the latent space of a diffusion model during reverse sampling, our method operates directly on high-level semantic representations, thereby resolving the effectiveness-utility bottlenecks by construction. We further ground our optimization with GeoCLIP, a model explicitly aligned with GPS coordinates, as a surrogate to pinpoint and disrupt the geographic signals that MLRMs exploit for location inference. This targeted semantic disruption yields significantly stronger black-box transferability while preserving perceptual image quality, offering a seamless integration on social media platforms.

Masked discrete diffusion models are commonly accelerated using the so-called tau-leaping discretization method, which reveals several coordinates in parallel at each sampling step. The sampler replaces the joint conditional law of each revealed block by a product distribution, incurring a factorization error $\varepsilon_\text{fact}$ present even with perfectly learned predictors. We analyze the standard sampler on $N$ coordinates with $K$ sampling steps, whose random block sizes depend on a denoising schedule. Our analysis uses an exact integral representation of $\varepsilon_\text{fact}$ in terms of a distribution-dependent dependence density $ρ$, which records how conditional dependence evolves as the revealed fraction of coordinates grows. We develop estimators for this profile and quantify how estimation errors affect schedule selection. We derive recursive stationarity equations for the finite-$K$ optimization problem and, under a monotonicity condition, characterize its unique optimizer. In the joint limit $N,K\to\infty$, we obtain an explicit characterization of the optimal limiting smooth schedule and quantify the cost of random block sizes relative to a deterministic planner. When $ρ_N$ converges uniformly to a strictly positive continuous profile, optimizing over fixed smooth schedules can improve the leading constant but not the $N/K$ scaling of $\varepsilon_\text{fact}$. By contrast, if $ρ_N$ degenerates, suitable schedules can improve the asymptotic order relative to the uniform schedule. Examples based on stationary processes and exchangeable mixtures illustrate these two regimes.

Quantization offers a practical path to deploying diffusion models with reduced memory and computation, but aggressive compression can cause quantized outputs to deviate substantially from their full-precision counterparts. Sampling-stage correction methods seek to compensate for such deviations during sampling, but existing approaches rely primarily on local information and underexploit trajectory history, limiting their ability to correct errors that propagate across timesteps. In this work, we formulate sampling with a quantized denoiser as an online estimation problem, using the history of quantized denoiser outputs to recover the underlying full-precision outputs required by the sampler. We propose QuAKE, a Quantization-Aware Kalman Estimator that combines a smooth trajectory prior with a conditional Gaussian observation model. At each sampling step, QuAKE recursively updates the posterior over the output window in closed form and feeds its posterior mean to the sampler. QuAKE is a lightweight plug-and-play corrector that requires no modification to the quantized network and naturally supports arbitrary high-order multistep ODE samplers. Experiments across W4A4-quantized text-to-image diffusion models show that QuAKE consistently outperforms existing methods in reducing the distributional discrepancy from full-precision sampling.

Best-of-$n$ (BoN) sampling is a simple yet effective inference-time alignment method, but hard maximization provides only coarse control over the trade-off between reward and distribution shift. Soft Best-of-$n$ (Verdun et al. 2025) provides smoother control and converges to the optimal distribution associated with KL-regularized reward maximization. In this paper, we introduce ExpBoN, an alternative soft BoN method based on the exponential-noise report-noisy-max mechanism. It admits an exact finite-$n$ decomposition, which yields exponentially fast convergence in total variation, expected reward, and both directions of KL divergence. We provide comprehensive theoretical analyses of its convergence and regret behavior. We further integrate ExpBoN into the guided speculative inference (GSI) framework (Geuter, Mroueh, and AlvarezMelis 2025), resulting in ExpGSI, for efficient reward-guided LLM alignment. ExpGSI yields substantial reductions in computational cost while maintaining comparable accuracy. Experiments on MATH500, MMLU-STEM, and Minerva Math with the Qwen2.5-Math and Qwen3 model families show that ExpGSI reduces estimated computation by $14%$-$39%$ across candidate budgets for Qwen2.5-Math and by up to $45%$ at $n=16$ for Qwen3. Overall, our results provide a theoretical and algorithmic foundation for exponential-noise BoN and efficient test-time LLM alignment.

Federated learning (FL) enables collaborative model training without sharing raw data, but its performance degrades under non-IID data and stochastic client participation. Remedies built on classical Federated Averaging (FedAvg) typically presuppose that client participation probabilities are known to the server, which is rarely the case in deployed systems. We first discuss and then characterize the optimization problem that distributionally agnostic FedAvg actually solves when participation is entirely unknown, possibly highly skewed, and of variable size across rounds: uniform aggregation is shown to minimize a well-defined stochastic objective, weighted by the participation-induced marginal, at a standard $\mathcal{O}(1/\sqrt{T})$ rate for convex and possibly nonsmooth losses. Building on this characterization, we propose Federated Risk-Averse Averaging (\textsc{FedeRage}), a risk-averse extension of FedAvg that embeds the Conditional Value-at-Risk (CVaR) into the local objective within a natural distributionally robust optimization (DRO) framework. \textsc{FedeRage} implicitly upweights high-loss and infrequently participating clients while adding only a single scalar per-client, and admits an $\mathcal{O}(κ/\sqrt{T})$ rate in which the factor $κ$ is the upper bound on the ``price" of risk aversion. In contrast with aggregation-alignment schemes based on optimal transport, which require the availability distribution as an input, \textsc{FedeRage} remains agnostic to it. Several experiments on three heterogeneous benchmarks indicate consistent improvements over state-of-the-art methods in accuracy, fairness, and convergence speed.

Image diffusion models have shown impressive image generation capabilities but are often hard to control, in contrast to classical computer graphics pipelines such as physically based rendering. However, we observe that there is a bridge between light transport phenomena and the distribution of latent space values produced by such models. Thus, we introduce physically based rendering in the feature space learned by the variational autoencoders in generative models, enabling light transport simulation in the latent space. This allows us to leverage physically based rendering techniques to output latent maps for physically guided content generation. We propose modifications to the rendering equation, which, when paired with a differentiable renderer, can yield an optimal set of scene parameters that require only minimal refinement to accurately render into the pretrained latent space. We train our method on a single rendered image, and then demonstrate the generalization of the method to scene geometry changes, lighting changes, and camera view changes.

Satellite communications are an essential component of sixth-generation (6G) mobile networks, which provide ubiquitous connectivity for global services. However, the satellite uplink remains a critical bottleneck for ground devices: their limited transmit power and antenna apertures result in low data rates and high packet errors. To overcome this bottleneck, this paper advocates a novel relaying paradigm termed generate-and-forward (GF) communications, where satellites exploit on-orbit generative artificial intelligence (AI) to robustly reconstruct corrupted data prior to forwarding. Specifically, we propose SpaceDiffusion, an over-the-orbit diffusion framework for satellite-assisted image transmission. The core of this framework is a channel-distortion-aware diffusion theory developed using the following approach. By formulating the recovery of compressed and lost image tokens as an inverse problem, this theory incorporates a channel-distortion correction term directly into the conventional denoising diffusion implicit model (DDIM) update. As a result, this design enables a single pretrained diffusion model to adapt dynamically to varying packet-loss patterns and compression distortions without retraining. Furthermore, we analytically characterize the progressive token-reconstruction error and derive a diffusion-step activation threshold that predicts when SpaceDiffusion is expected to outperform conventional decode-and-forward (DF) relaying. Building on these theoretical insights, we further develop an energy-aware early-exit policy to efficiently deploy SpaceDiffusion in orbit. Experimental results demonstrate that SpaceDiffusion achieves lower end-to-end latency compared to DF scheme with retransmission protocol and saves approximately 15 dB of uplink transmit power at a target perceptual quality.

The existing singularity-free guiding vector field (SF-GVF) with an additional virtual coordinate can eliminate singular points (i.e., points where the vector field vanishes) inherent in conventional GVFs and guarantee global convergence of robot trajectories to closed and self-intersecting desired paths. However, the desired speed given by the GVF along the desired path in the original lower-dimensional space cannot be arbitrarily specified but depends on path parameterizations. One possible workaround is to partially normalize the physical projection of the SF-GVF and assign a user-designed speed. However, we show that this workaround may introduce new singularities since the normalization denominator can become zero. To address this issue, we propose a new SF-GVF with prescribed physical speed (PPS). The integral curves of the new SF-GVF converge exponentially to the desired path from any initial condition in the higher-dimensional space (including virtual dimension); more importantly, the robot's physical speed converges to the PPS, while the path-error dynamics remain invariant under regular reparameterizations of the desired path. We further develop a saturated acceleration control law for second-order kinematic models. Finally, comparative simulations and 3D path-following experiments with a quadrotor under different PPS profiles validate the theoretical results and demonstrate the effectiveness of the proposed approach.