生成模型理论与方法

Generative models have found great success as data-driven methods of solving inverse problems. Two popular approaches work either by combining a pretrained generative prior with a known degradation model, or by training a conditional generative model directly from paired data. We target a setting that spans both regimes: unknown degradations can be learned from few paired examples, while known degradations can be learned from self-generated samples. We introduce Likelihood Score Approximation (LSA), a generative framework that keeps a pretrained unconditional model fixed and learns an observation-conditioned model that approximates the likelihood score from paired samples. Within a conditional stochastic-interpolant framework, LSA can be trained in either score or velocity coordinates, independently of the unconditional model's native parameterization, and supports both deterministic and stochastic sampling. We further show empirically that the prior model can be swapped post-training while keeping the same LSA model. Across speech and image inverse problems, LSA operates effectively even at roughly 0.01% of the full training dataset. On the ImageNet-256 benchmark it achieves competitive or better restoration quality than strong posterior-sampling baselines while requiring up to several orders of magnitude fewer network evaluations.

Flow matching (FM) learns generative dynamics through velocity regression. Geometric FM variants commonly assume a prior supported on the data manifold, requiring geometric knowledge that is often unavailable. Without such knowledge, low regression error alone does not guarantee manifold adherence. Adherence keeps generated samples within valid configurations and is empirically associated with better task performance. We introduce manifold-stable flow matching (MSFM), which can start from an arbitrary ambient prior, not necessarily supported on the manifold. Using tools from nonlinear dynamics, namely contraction theory, MSFM combines learned tangential transport with prescribed normal contraction. The construction uses analytical projectors for known manifolds and local affine proxies estimated by principal component analysis for unknown data geometry. By implementing contraction theory in both cases of known and unknown manifolds, we guarantee manifold invariance and transverse convergence to the manifold within a desired time window (e.g., one second). We derive a family of compatible probability paths and decompose the training loss into a learnable tangential term and a normal residual. An ellipse experiment attains a mean terminal off-manifold error of order $10^{-6}$. In Push-T robotic experiments, MSFM raises success from $74%$ to $82%$. In the Robomimic Square task, success increases from $60%$ to $72%$, while rotation-manifold deviation decreases from order $10^{-2}$ to $10^{-7}$. The MSFM terminal geometric errors are controlled by the chosen numerical tolerance. These results demonstrate stronger geometric adherence and higher observed task performance, supporting prescribed normal contraction as a complement to learned generative transport.

Many inference-time tasks for pretrained discrete diffusion models and diffusion language models reduce to drawing samples from a tilted version of the pretrained distribution. Feynman-Kac sequential Monte Carlo (SMC) makes this correction exact in principle, but its prescribed weights routinely degenerate when the proposal dynamics are misaligned with the tilt, capping the practical gains from additional particles. We introduce FluxLite, a lightweight, training-free proposal-control framework for discrete diffusion. On the sparse directed graph of pretrained reverse rates, any sparse jump-rate perturbation can be exactly compensated by a $q_t$-weighted graph-divergence term in the Feynman-Kac potential; the target path is therefore preserved while the residual reweighting variance becomes a local convex objective. We instantiate this principle as two practical samplers: a one-hop local reallocation rule (HEU) and a small nonnegative quadratic program over pretrained-rate bases (D-VCG). We further prove population stability under the standard score-entropy training loss, identifying a tilted-path coverage factor that governs robustness to score error, together with finite-particle convergence for a fixed controlled Feynman-Kac recursion. Empirically, FluxLite improves over standard Feynman-Kac SMC baselines by up to two orders of magnitude in terminal KL on an analytically tractable finite-state CTMC benchmark, and reduces row-correlation MSE on 2D Ising sampling by 5-7x in geometric mean and up to 55x at peak.

Generative and representation learning remain asymmetrically connected: semantic representations are used to improve diffusion generation, whereas the models' own representations are often treated as a by-product of synthesis. We ask whether diffusion models can instead be trained to learn substantially stronger semantic representations without sacrificing generation quality. SelfFlow takes a step in this direction by introducing self-supervised patch alignment into flow matching, but its main gains remain in faster convergence and improved generation. Inspired by DINO and iBOT, we extend this framework with cross-view class-token alignment to further strengthen semantic representations. Specifically, we form two independently noised, dual-timestep observations of each image and align each student class-token representation with the stop-gradient EMA-teacher target from the other observation. This objective is optimized jointly with the inherited flow-matching and local patch objectives. Notably, although the additional objective acts only on the class token, it strengthens both class-token and patch representations. Compared with a matched two-view baseline, ImageNet linear-probing accuracy improves by 9.4% using the class token and 10.1% using mean-pooled patch tokens, while frozen-backbone VOC2012 segmentation improves by 3.6 mIoU. These representation gains are achieved while maintaining comparable ImageNet generation FID. In text-to-image training, the same objective also improves generation FID, reducing it from 2.52 to 2.37 at matched checkpoints. Our results show that representation need not remain a by-product of generation or merely a tool for improving it: it can be directly optimized as a first-class capability of diffusion pretraining alongside generation.

D-peptides combine protease resistance with high target specificity, but computational design of D-peptide binders remains immature. Mirror-Peptidizer introduced an in silico mirror-image screening pipeline using target reflection, backbone generation, and ProteinMPNN sequence design, but its raw ProteinMPNN negative log-likelihood (NLL) ranking was not validated against measured affinities, and only 4 of 9 tested MDM2 designs bound detectably. We introduce Mirror-Score, a calibrated, inference-only scoring framework for heterochiral D-peptide/L-protein complexes, and a public benchmark of 31 crystal complexes across four target families, including 18 with literature-verified affinities. Raw ProteinMPNN NLL is not a valid affinity ranker: its pooled Spearman correlation with affinity is 0.19, and correlations reverse between MDM2/CHIP (+0.62) and gp41 (-0.70). We therefore evaluate Boltz-2 mirror-space cofolding confidence. For the complete viral-entry family (7 structures representing 3 peptides), interface predicted local distance difference test (pLDDT) achieves structure-level leave-one-out Spearman rho = 0.90 (p = 0.006) and correctly orders all three peptides by affinity, whereas NLL fails (structure-level rho = 0.18). Because only three independent chemotypes are represented, this result indicates directional consistency rather than a statistically validated predictor. Cross-family calibration does not transfer at current sample sizes, supporting family-matched calibration as the practical deployment mode. We also specify a prospective design protocol for the antimicrobial-resistance targets LasR and LecB from Pseudomonas aeruginosa, including mirrored structures, ligand-derived hotspot maps, diffusion-model-ready inputs, and Mirror-Score ranking. Code, benchmark data, structures, and analysis scripts are openly available at https://github.com/Jiadalee/Mirror-Score.

Discrete diffusion models generate sequences by iteratively resolving multiple tokens in parallel, offering a flexible alternative to left-to-right generation. However, guiding this process with a sequence-level objective is difficult because the value of one unresolved token depends on the other tokens with which it can form a high-reward sequence. Enumerating all such completions makes the whole guidance computation grow exponentially with the number of unresolved positions. We introduce COFFEE, a plug-and-play framework that avoids this enumeration by separating sequence dependence from the objective. At each diffusion step, a target-free carrier absorbs the marginal token distributions predicted by the denoiser to construct a joint model over the unresolved tokens, while a compiled finite-state model records how their combinations affect the sequence-level preference. Pairing their states allows COFFEE to transfer global preferences to unresolved positions and sample a clean reconstruction without retraining the diffusion model. The same framework supports explicit hard constraints and learned soft objectives. We evaluate COFFEE across multiple symbolic, language, and biological benchmarks, where it achieves strong control results with task-dependent quality and diversity trade-offs. By making objectives available to inference rather than only evaluation, COFFEE brings joint conditioning, completion-weighted guidance, and optimization-based constraints into pretrained neural generation, showing the potential of neural-symbolic methods in diffusion guidance.

Multi-step matching models, including flow and diffusion models, produce high-quality outputs but incur substantial inference costs and may reproduce unwanted components of their training datasets. We introduce Inverse Distillation Unlearning (IDU), a unified framework that simultaneously distills a teacher multi-step matching model into an efficient one-step student generator and suppresses outputs corresponding to a designated training subset. We first formulate distillation as a min-max objective over a data distribution and then represent this distribution as a mixture of the forget-set and the generated distributions. This allows us to compare this mixture with the teacher's training distribution and recover only the retained data at the optimum. Our method requires only a pretrained full-data teacher and data from the forget set, without access to retained training examples, extra feature extractors or classifiers. Extensive experiments on MNIST and CIFAR-10 datasets under flow-matching and score-based diffusion settings demonstrate that IDU substantially reduces the generation frequency of forgotten classes while preserving generation quality on the retained classes. To the best of our knowledge, IDU is the first unified framework for simultaneous unlearning and distillation in unconditional flow-matching and score-based models.

Latent reward models (LRMs) enable efficient alignment of video diffusion models by scoring intermediate states directly in latent space. However, we find that optimizing against a fixed latent reward rapidly leads to latent reward hacking: the predicted reward stays high while perceptual and motion quality deteriorate. Our analysis identifies distributional escape as the central cause: within a few hundred updates, the generator moves beyond the reward model's training support, where its scores no longer reflect video quality. Based on this insight, we introduce CoRe, a co-evolving reward framework that treats latent-space alignment as a dynamic interaction between the generator and the reward model. Rather than optimizing against a stationary proxy, CoRe continually refits the reward model on the generator's current samples while anchoring it to real-video preferences, so the generator cannot gain reward by drifting away from the data. On Wan2.1-T2V-1.3B, experiments show that CoRe consistently improves generation quality over both the pretrained model and prior alignment methods, while avoiding the quality collapse of fixed-reward optimization.

Diffusion models can produce striking images and videos, but they still struggle with the compositional details that make a generation faithful to a prompt, such as object counts, attribute binding, spatial relations, and temporally grounded actions. A common way to improve prompt satisfaction is to spend more compute at test time through Best-of-N sampling, but final-sample selection is fixed. Best-of-N can only choose among completed outputs and cannot repair a promising trajectory before it fails. We introduce PreviewDiff, a training-free test-time search method that turns diffusion sampling from scalar search into a multimodal critic-guided search over intermediate latents. At selected denoising checkpoints, PreviewDiff decodes a partial preview, asks a multimodal judge to score and critique it, and uses the resulting natural-language feedback to branch over semantic prompt edits and locally re-noised latent continuations. These branches are then scored and selectively rolled forward, allowing verifier compute to guide generation while the sample is still editable. Across image and video generation benchmarks, PreviewDiff consistently improves over budget-matched Best-of-N selection and strong scalar-search baselines. Ablations show that earlier interventions and increased search width provide the largest gains, while deeper search and additional semantic variants offer complementary improvements. PreviewDiff demonstrates that multimodal feedback is most useful not only as a final verifier, but as an active controller inside the denoising process.

Gradient-based reward guidance provides a flexible way to use downstream reward models to control masked diffusion language models at inference time. However, its computational cost remains high as each decoding iteration incurs expensive diffusion model forward passes and reward model backpropagation steps. To address this, we introduce FastGuide, an adaptive hybrid of parallel and autoregressive decoding to accelerate reward guidance for diffusion language models. In analogy to parallel decoding, FastGuide amortizes the cost of reward model backpropagation by computing guidance once per decoding step and reusing it to generate multiple tokens. Within each decoding step, FastGuide makes diffusion forward passes autoregressive by unmasking tokens one at a time while efficiently recomputing token distributions after each unmasking by utilizing KV caching techniques and sparse recomputation of attention. Lastly, to adapt hybrid decoding to the model's confidence, FastGuide defers any token that the model is unconfident about under its recomputed distribution. Experiments on three reward benchmarks demonstrate that FastGuide is up to $4.4\times$ faster than sequential reward-guided decoding while retaining similar generation quality.

Masked diffusion language models support arbitrary-order generation, suggesting a natural way to produce diverse outputs. However, recent work argues that this flexibility reduces diversity by delaying high-uncertainty tokens that can lead to different generation paths. We trace this diversity loss not to arbitrary-order generation itself, but largely to low-confidence remasking (LCR), a widely used decoding rule. At each step, LCR samples a token at every masked position but commits only the sampled token with the highest probability, filtering out the rest. We show that this mechanism can exponentially suppress lower-probability tokens as more positions compete, and observe the same suppression in LLaDA. In contrast, top-probability position selection (TPP), which has often been conflated with LCR under the shared label confidence-based decoding, avoids this diversity loss. TPP first selects the position whose most likely token has the highest probability, then samples directly from that position's distribution. Replacing LCR with TPP restores diversity and yields Pass@$k$ comparable to left-to-right decoding, suggesting that the reported diversity loss stems largely from LCR's filtering rather than from generating high-confidence positions first. To further exploit order flexibility, we introduce Entropy-Guided Initialization (EGI), which samples the first token at the highest-entropy position and then follows TPP. This simple modification further improves rollout diversity and solution coverage beyond left-to-right decoding, with gains extending to downstream policy optimization, highlighting the potential of arbitrary-order generation for diverse rollouts.

Pretrained autoregressive Transformers represent a large sunk investment in compute. Existing conversion methods reuse that investment by changing either the architecture (attention to recurrence) or the objective (next-token prediction to denoising), never both. We convert Qwen3 teachers at 1.7B and 8B into attention-free, bidirectional, gated-delta-rule diffusion students in three stages, so that each capability can be traced to the stage that kept or lost it. Language modeling transfers only partially and in-distribution; in-context retrieval does not transfer. On a multi-query recall probe where the teachers score 0.34-0.58, both converted students score 0.000, and diffusion pretraining alone does not restore retrieval. A retrieval curriculum in the final stage, which gradually lengthens the gap between a key-value table and the queries that address it, restores it only stochastically: on a fixed schedule, one seed in three learns to retrieve. Advancing the gap only while a running accuracy estimate stays above a threshold works for all three of those seeds, holds on real text, and carries unchanged to 8B, where two of three seeds succeed. The third had not learned within its fixed 16k-step budget: retrieval switches on abruptly at a seed-dependent step (6.5k and 11k in the other two), so a fixed budget can cut a late run off. One boundary survives every intervention: every model that learns retrieval scores 0.000 on tokens that never appeared in a retrieval episode, and an arm that resamples the key and value tokens every batch shows this is a coverage limit, not memorization of particular bindings. Separately, we convert a 7B code model into a 3:1 recurrent-attention block-diffusion hybrid over 85k steps and report two negative training results.

Large language models (LLMs) typically generate text autoregressively (AR), predicting one token at a time. Block diffusion language models (dLLMs) instead generate blocks sequentially while denoising multiple tokens in parallel within each block, offering a promising way to accelerate generation. Rather than training such models from scratch, recent work adapts strong pretrained AR models into block dLLMs through distillation. On-policy distillation (OPD) has been widely used for LLM training because it supervises the student on states generated by its current policy, rather than only on fixed offline trajectories. By training on the states the student actually visits, it reduces the mismatch between training and generation and can provide more relevant supervision as the student evolves. Recent work has extended this idea to AR-to-block-diffusion conversion. However, this setting introduces a fundamental mismatch in supervision: the block-diffusion student and the causal AR teacher condition on different information at the same training state. The student predicts from the entire partially denoised block, including visible future context, whereas the standard AR teacher target is defined only from the causal prefix. As a result, the teacher distribution used for distillation is not fully aligned with the information available to the student. We therefore introduce d-OPD, a future-aware on-policy distillation method that corrects the AR teacher distribution to better align with the student-visible state by incorporating visible future information within each block, providing supervision that better matches the information used by the student. Across Qwen3 models from 0.6B to 8B, d-OPD improves the six-benchmark average by up to $4.0$ points over OPDLM and reduces training time by $1.35$-$1.58\times$. The code is available at https://github.com/mit-han-lab/d-OPD.

Diffusion and flow-matching models can produce high-quality posterior samples for inverse problems, but typically require tens to thousands of network evaluations per draw. MeanFlow enables one-step generation, yet applying it to inverse problems leaves no intermediate steps at which to enforce measurement consistency. We introduce SNaP, a one-step MeanFlow posterior sampler for linear inverse problems with Gaussian noise. Its central innovation is a measurement-adapted source: a Gaussian distribution whose mean and anisotropic covariance are determined by the measurement operator, observation, and noise level. The source anchors well-measured directions while preserving variation where the measurements are weak or uninformative. We show that the exact conditional flow transports this source to the true posterior. Across natural-image restoration and multi-coil MRI, SNaP produces diverse, high-quality samples with one network evaluation per draw, 30 to 2250 $\times$ faster than iterative samplers.

Schrödinger bridges provide an entropy-regularized framework and a principled solution for unpaired domain translation. In practice, a pretrained bridge may need to be adapted to human preferences or physical constraints through a reward a problem closely related to reward tilting in diffusion models but underexplored for Schrödinger bridges. We introduce Tilted Schrödinger Bridge Matching (TSBM), a post-training method for fine-tuning a learned bridge $P$ between source $p_0$ and target $p_1$ toward a reward-tilted target $p_1^r\propto p_1e^r$, while preserving source $p_0$. We formulate this adaptation as alternating optimization initialized from $P$, provide theoretical justification, and derive a practical algorithm based on Adjoint Matching. We evaluate TSBM on unpaired image-to-image translation targeting digit properties in MNIST and facial attributes in CelebA.

Text-to-motion generation and motion-to-text captioning are two fundamental tasks in human motion modeling, both grounded in the same underlying motion-text correspondence. Existing unified approaches mostly rely on autoregressive modeling, which imposes a fixed generation order and is therefore poorly suited to the bidirectional dependencies between language and motion, allowing early prediction errors to persist as fixed context and degrade both temporal coherence and cross-modal consistency. Masked discrete diffusion, which models sequences through iterative bidirectional prediction, offers a natural remedy. We therefore propose BiMoGen (Bidirectional Motion-text Generation), a unified masked discrete diffusion framework for bidirectional motion-text modeling. To stabilize training, we design Decoupled Uni- and Cross-Modal Training, in which masked pretraining first establishes cross-modal correspondence on paired motion-text sequences, after which supervised fine-tuning specializes the model for bidirectional generation. Masked diffusion nonetheless introduces its own source of error, as the model is trained on clean ground-truth context yet encounters self-generated and potentially erroneous context at inference, with errors committed under heavily masked states propagating through subsequent steps. We further introduce Generation-Aware Self-Correction that exposes the model to its own predictions during training and applies correction passes at early sampling steps to revise unreliably committed tokens. Extensive experiments on HumanML3D and KIT-ML demonstrate competitive performance on both tasks, validating the effectiveness of the proposed two-stage training and self-correction designs. The project page is available at https://wengwanjiang.github.io/BiMoGen-Page.

Distributional training provides collective supervision for one-step visual generation by matching real and generated features in frozen representation spaces. We introduce a unified theoretical framework that separates distribution modeling from matching discrepancy and connects global objectives to pointwise feature updates through Wasserstein gradient flow. Under this framework, FD-Loss and Gaussian-kernel Drifting are recovered through Gaussian optimal transport and kernel-density-based KL matching, respectively. The framework motivates MGFlow, which models feature distributions with Gaussian mixtures at an adjustable granularity between global moments and sample-based representations. MGFlow supports both optimal transport and score-based matching, and couples mass-constrained sample assignment with paired component updates to address mode collapse that mixture expressivity alone does not resolve. On ImageNet $256\times256$, MGFlow substantially surpasses the FD-Loss baseline, achieving state-of-the-art results with 1.45 $\mathrm{FDr}^6$ on pMF-H and 1.64 on JiT-H. For text-to-image generation, MGFlow post-trains FLUX.2 [klein] 4B into a one-step generator that outperforms the original four-step model on both GenEval and PickScore.

The rising number of concept unlearning techniques for text-to-image (T2I) diffusion models has produced a fragmented evaluation landscape. Methods are assessed under heterogeneous experimental conditions making principled cross-method comparison difficult. We present eval-unlearn, an open-source Python library providing a unified, reproducible benchmarking framework for concept unlearning in T2I Diffusion models. eval-unlearn integrates twelve published unlearning techniques spanning fine-tuning, closed-form model editing, and inference-time intervention, alongside nine complementary evaluation metrics covering erasure efficacy, adversarial robustness, generative quality, and concept retention. Its plugin architecture lets third-party techniques and metrics self-register without modifying the core framework, and its streaming, batched pipeline supports efficient evaluation of both standard NSFW concepts and arbitrary general concepts. As a further contribution, we release a public leaderboard on HuggingFace along with an interactive tool for real-time evaluation of unlearning techniques. The leaderboard compares nudity concept erasure case study across all twelve techniques, exposing significant accuracy-quality trade-offs that are obscured by heterogeneous evaluation. eval-unlearn is released under the MIT license; the package, code, leaderboard, and documentation are all available at https://eval-unlearn.readthedocs.io.

Self-training generative models - the continued improvement of a model using its own outputs - is becoming increasingly important as high-quality training data becomes scarce. However, naively finetuning on model-generated samples leads to degradation through model collapse and the model autophagy disorder. Negative-guidance self-training methods turn this degradation into a useful signal, using a model finetuned on its own outputs to guide the original model toward improved generation. Existing methods, however, take the negative signal in standard model outputs as given. We instead ask whether this signal can be explicitly strengthened. We introduce Geometrically Modified Outputs (GMOs), which reweight the singular values of the generator's input-output Jacobian to increase the influence of its leading singular directions. This geometric modification amplifies the mode-seeking behavior and distortions of standard outputs, providing a stronger and more targeted negative signal for self-training. Across a range of one-step generative models, GMOs consistently improve the performance of negative-guidance methods, including Neon and SIMS, compared with using standard model outputs.

Novel view synthesis from sparse images must reconcile faithful reconstruction of observed regions with plausible completion of unseen content, while maintaining world consistency across viewpoints. Existing geometry-based methods preserve observed scene structure but often struggle to complete unseen regions, whereas video generative models offer rich appearance priors but accumulate inconsistencies during sequential view generation. We propose GeoVerse, a framework that synthesizes world-consistent novel views by performing generation within the geometric latent space of a pretrained 3D foundation model and injecting appearance priors from a video generative model. Specifically, GeoVerse extracts multilevel features from Wan2.2 VACE and injects them into the geometric latent diffusion model via a ControlNet-style adapter, incorporating video-learned appearance priors to enhance structural completion. To enforce cross-view coherence, a global spatial memory continuously aggregates observed and synthesized content, reprojecting target-aligned guidance to anchor subsequent predictions to a shared scene representation. Extensive experiments across diverse datasets demonstrate improved visual quality and geometric consistency, with a 2.23 dB higher PSNR on DL3DV and 32.4% lower ATE on Mip-NeRF360 compared to GLD.

On-policy distillation (OPD) specializes pretrained video diffusion models through teacher supervision along the student's own generation trajectory. Although large video models are natural teachers, developing specialized video experts can require costly video data and training, while querying them incurs substantially higher latency than querying image experts. More readily available and cheaper to query, image experts offer a cost-effective alternative, particularly for largely temporal-agnostic capabilities such as aesthetics and OCR that admit frame-level supervision. However, heterogeneous image and video latent spaces prevent direct supervision of intermediate student states, while image experts lack cross-frame motion supervision, making temporal consistency vulnerable to frame-level improvements. In this paper, we propose MILD, a Motion-Preserving Image-to-Video Latent Distillation framework that transfers specialized image expertise while preserving pretrained video dynamics. MILD uses a learnable linear connector that aligns student latent states and predicted updates with those of image experts, enabling supervision transfer across heterogeneous latent spaces. We further constrain image-guided corrections around the pretrained student's predictions to preserve video dynamics and incorporate an optical-flow-based motion reward to improve motion quality and temporal consistency. Across specialized image experts and multiple video-student backbones, our method consistently outperforms video-teacher OPD baselines, with further studies demonstrating effective transfer across connector designs and heterogeneous architectures. These results establish image-to-video distillation as an effective route to improving video generation by drawing on the diverse and evolving capabilities of the image-generation ecosystem.

Few-step generative models can generate high-fidelity samples within a few function evaluations. Despite this efficiency, generated samples may not exhibit desirable properties. When these properties are difficult to encode as an explicit reward function, direct preference optimization (DPO) can align generative models using pairwise preference feedback without training a separate reward model. However, extending DPO to few-step generative models is challenging because few-step generative models are generally implicit, making the likelihood evaluation required by DPO intractable. To address this challenge, we introduce Few-step DPO (FestDPO), an extension of DPO for few-step generative models that leverages nonparametric likelihood estimation from empirical samples. By exploiting the fast sampling capabilities of few-step generative models, our approach makes sample-based approximation of DPO loss computationally feasible. Furthermore, the sample-based formulation makes FestDPO agnostic to the model family and sampling procedure. Our toy experiment demonstrates that FestDPO matches the reward-tilted target distribution across four few-step generators. For real-world tasks, we evaluate FestDPO in two domains: text-to-image generation and protein backbone generation. In text-to-image generation, FestDPO outperforms preference optimization baselines in both win rates against the base models and human evaluation scores. In protein backbone generation, it achieves a higher $β$-sheet fraction and better structural designability than the baselines.

Discrete diffusion models offer the ability to re-draft, revisiting and correcting earlier tokens throughout generation. This capability depends on the forward corruption process that defines what the denoiser learns to correct. Masked diffusion models fix tokens once they are unmasked, while uniform diffusion permits revisions but relies on uniformly random token substitutions. We instead learn which substitutions are most useful for training the denoiser to re-draft. We introduce Variational Stackelberg Discrete Diffusion (VSDD), a framework for learning a semantically aware corruption process. VSDD formulates training as a leader-follower game: the leader defines a Markovian corruption process parameterized by the denoiser's token embeddings, while the follower optimizes a variational denoising objective with the corruption process held fixed. The leader rewards corruptions based on how much the denoiser improves after learning from them, rather than on how easily the current denoiser can reconstruct them. We measure this improvement under a fixed reference corruption process, approximate the follower's response with a one-step gradient update, and optimize the leader using a score-function estimator. We evaluate VSDD across molecular, text, and playlist generation. VSDD substantially improves molecular validity over uniform and masked diffusion, reduces text perplexity relative to uniform diffusion while remaining competitive with masked diffusion, and achieves sizable improvements in offline playlist recommendation metrics.

Score-based generative models generate new samples by integrating a time-dependent drift that carries Gaussian noise onto the target distribution. In practice this drift is modeled by a neural network, trained on a loss integrated over time $t$ with a weighting schedule $w(t)$. Along the backward dynamics, and for multi-modal distributions, trajectories commit to modes of the target within a narrow time window, the speciation time. In this work, focusing on high-dimensional data, we decompose the integrated loss into its single-time contributions and analyze each at fixed signal-to-noise ratio $Λ(t)$: we show that $Λ(t)$ sets the rate at which each feature of a multimodal target - the mode directions and their relative weights - is acquired during training. Crucially, at high $Λ(t)$ all mode directions are acquired together, on a single timescale insensitive to their amplitudes, while the relative weights are not learned at all. Only near the speciation time, where $Λ(t)$ becomes of order one, do all features become learnable, each on its own timescale: the weights are acquired jointly with the directions, and the directions at rates set by their relative amplitudes. For models trained on time-integrated objectives, the learning dynamics is then governed by how much of the weighting effectively sits near the speciation time, which provides insights on $w(t)$ design choices. These results follow from an exact high-dimensional analysis of the training dynamics of unbalanced and hierarchical Gaussian mixtures. Numerical experiments on image and human genome haplotype generation recover the predicted hierarchy of learning timescales in more complex settings.

As the world moves towards sustainable energy sources, hydrogen (H2) can be treated as an eco-friendly alternative to fossil fuels due to its high energy density and zero carbon emissions. The water-gas shift (WGS) reaction is a widely used industrial process for hydrogen production by converting carbon monoxide and steam into hydrogen and carbon dioxide. However, occurrences like severe fouling, catalyst deterioration, and thermal runaway can hamper the reaction kinetics/process safety and decrease the yield of H2. These incidents are rare, and gathering process data under such abnormal conditions is challenging. In this work, we propose a physics-guided conditional diffusion model to generate realistic rare-event trajectories for the WGS reaction. The proposed model integrates a conditional denoising diffusion probabilistic model (CDDPM) with governing laws of the reaction to generate physically consistent process trajectories. The conditioning features allow the model to produce high-quality synthetic profiles for rare-event domains that are typically beyond the training regimes. The generated rare-event trajectories then augment the raw dataset for a balanced distribution between normal and abnormal conditions. We further propose a hazard score to assess the risk severity of the operating condition based on the operating trajectory. Deep learning models are trained with the augmented dataset to diagnose the health status of the reaction. Simulation results show that the proposed physics-guided diffusion model outperforms data-driven models in terms of the quality of synthetic data and diagnosis performance for rare events.

Modern video diffusion models require tens of denoising evaluations over long spatiotemporal token sequences. Distribution Matching Distillation (DMD) reduces the number of function evaluations (NFE) to just a few. However, DMD samples can degrade during training, exhibiting progressive oversaturation and artifacts. We trace this instability to critic errors, which enter successive student updates and accumulate over time. We introduce Projected Distribution Matching Distillation (PDMD) to filter critic errors. PDMD projects out the component of the DMD update parallel to the student-critic endpoint residual. At a fixed noisy query, we prove that this residual is an unbiased estimate of the critic's endpoint error. Under high-dimensional assumptions, this projection removes a constant fraction of critic error while discarding only a vanishing fraction of ideal DMD signal. Empirically, the projection stabilizes training and improves sample quality where DMD degrades and develops unnatural textures. PDMD requires only a one-line code change to DMD, with no extra loss, network, data, model pass, or multi-stage training. With Wan2.1, PDMD achieves a VBench total score of 83.73 at 4 NFE, surpassing matched DMD by 1.03 points. On MiniMax-H3 joint video-audio generation, PDMD achieves a VideoGen-Eval visual total score of 83.17, 0.41 points above the strongest distilled baseline. PDMD also achieves the best performance on all six audio metrics among the compared 4-NFE models. Qualitative comparisons and user studies favor PDMD over the distilled baselines in visual quality, motion, and audio quality. Code and models are available at https://pdmd2026.github.io/.

Long-horizon micromagnetic simulation remains expensive because conventional and learned solvers typically propagate Landau--Lifshitz--Gilbert (LLG) dynamics step by step. Existing learned approaches generally retain stepwise integration or model deterministic evolution, leaving full-field, direct-horizon stochastic prediction largely unexplored. We propose FLARE, a flow-matching framework that recasts stochastic finite-time magnetization prediction as conditional transport over anchor-relative local axis-angle rotations. This rotation-space formulation respects the intrinsic geometry of magnetization dynamics and preserves pointwise unit norm by construction. By explicitly conditioning on the physical prediction horizon, FLARE directly generates full-field stochastic endpoints across multiple target times without stepwise integration. Against the strongest single-checkpoint external baseline on each metric, FLARE achieves 29.9% lower angular energy distance ($15.30^\circ$), and a 37.3% lower fair energy score (0.393). On a representative composed 5-ns two-segment protocol, FLARE achieves a $3{,}062\times$ best-batch speedup over the widely used GPU micromagnetic solver MuMax$^3$ on a single GPU.

Constrained decoding for Masked Diffusion Language Models (MDLMs) aims to ensure that generated outputs satisfy a specified structure or syntax constraint. MDLMs generate outputs by repeatedly unmasking masked positions present in their current state. Recent strategies for constrained decoding constrain the model's per-step mean-field posterior (which factorizes over masked positions) by enforcing the desired constraint with an automaton. The resulting chain-structured factor graph allows exact constrained sampling via dynamic programming. However, despite each draw being exact and constraint-satisfying, we prove that their composition, in general, tilts away from the model's relative probabilities over valid trajectories, thus leading to trajectory bias. We derive an exact expression for this bias as a product of ratios measuring how valid continuation mass changes when the denoiser is reconditioned, and characterize when the bias vanishes. We then correct the bias by introducing TWISTER, the first automaton-twisted Sequential Monte Carlo decoder for MDLMs, using the step-exact decoder as the proposal. We show that for regular language constraints, the Feynman-Kac correction is exactly computable, with the twists obtained efficiently using quantities pre-computed for step-exact sampling. We prove that the resulting Feynman-Kac model targets the unbiased Doob h-transformed path law conditioned on constraint satisfaction.

Recent advances in diffusion and flow models have substantially improved text-driven human motion generation. Yet most methods generate in low-dimensional, temporally downsampled latent spaces learned primarily for reconstruction, a bottleneck that can limit generation quality and preclude direct manipulation of individual frames and joints. We introduce MotionSpaceFlow (MSFlow), a representation-aware flow-matching framework that predicts clean motion directly in continuous motion space without a learned encoder or decoder. To account for the anisotropic structure of direct motion representations, we propose representation-aware noise scaling and show how the initial Gaussian source scale governs the covariance of intermediate probability-path marginals. We further introduce a Representation-Aware Multimodal Diffusion Transformer (RA-MMDiT), which jointly updates token-level language and full-resolution motion features through joint attention while adapting temporal information flow to the motion representation: causal attention for incremental features defined by frame-to-frame changes, and bidirectional attention for global features such as absolute joint coordinates. Across different datasets and motion representations, MSFlow achieves state-of-the-art text-to-motion performance. Its global representation variant additionally enables zero-shot, inference-time control over any joint or frame through projection sampling without control-conditioned training, delivering leading motion quality with exact constraint satisfaction.

Diffusion models trained on a finite dataset first learn to generate novel, high-quality samples and only much later collapse onto their training set. We identify the mechanism behind this separation of timescales and the object that probes it. The training dynamics of the score function are governed---exactly, and at any width---by the Gram matrix of the Neural Tangent Kernel (NTK) evaluated on the noisy training data, so the timescales of generalization and of memorization must be encoded in its spectrum. We show that they are, and that the structure responsible has no analogue in standard kernel settings. The use of multiple noise realizations per sample ($m$ noised copies at a fixed noise level) in the score-matching loss is what restructures the Gram matrix spectrum into two distinct parts. The first, of large eigenvalues, carries the global features of the target distribution and is present already for $m=1$. The second, which the repeated noising creates, consists of the smallest eigenvalues and is supported on eigenvectors aligned with the sample-specific noise directions; it sets a memorization timescale parametrically larger in the training set size $n$. We establish this picture on two fronts. Analytically, we solve the spectrum in the lazy high-dimensional limit for both linear ($n \asymp d$) and polynomial ($n \asymp d^k$) sample complexities, and prove through a bias--variance decomposition that the first bulk minimizes the approximation error while the second drives the error associated with memorization. Empirically, we show the same two-bulk structure in Convolutional NTKs on CelebA and in finite-width U-Nets trained well beyond the lazy regime, and we make the link causal: truncating the Gram matrix at rank $r$ tunes the generalization--memorization transition, and an $L_2$ penalty targeting the second bulk suppresses memorization in feature-learning U-Nets.