生成模型理论与方法

Flow-matching models generate high-quality images and videos, but repeated neural network evaluations make sampling expensive. Skipping evaluations reduces this cost by extending an available velocity estimate over a longer span. However, local velocity agreement alone does not determine a suitable span, and checking each candidate endpoint adds costly model calls. We introduce ReAL, a training-free sampler that selects how far to advance using one shared lookahead. Our key insight is that the discrepancy between uncorrected and lookahead-corrected endpoint proposals can be computed directly from the observed velocity mismatch and the candidate span beyond the lookahead. This relation provides a span-dependent selection criterion without additional endpoint evaluations. The same lookahead selects the longest passing candidate span, corrects the accepted update, and supplies its velocity as the next starting estimate. After initialization, each regular iteration requires only one fresh evaluation. ReAL uses the pretrained velocity output and original noise schedule, with no additional training or access to internal features. Experiments cover four image-generation backbones, video generation, and image editing. ReAL achieves 4.91x measured speedup on FLUX.1-dev while retaining 97.0% of dense mean ImageReward. On HunyuanVideo, it achieves a 5.49x speedup while maintaining a VBench score close to that of dense sampling.

Conditional independence (CI) is a fundamental concept in statistics and machine learning. Recent advances in conditional generative modeling provide flexible tools for generative-model-based CI tests, which rely on an estimated conditional distribution to generate randomized samples. However, errors in estimating this distribution accumulate in existing Type I error bounds, and consistency of the generative estimator alone does not guarantee asymptotic Type I error control. To address this limitation, we formulate conditional generative modeling as a domain adaptation problem and leverage auxiliary data from multiple source domains to improve estimation in the target CI testing domain. We propose Domain-Adapted Diffusion (DA-Diff), a multi-source domain adaptation framework for conditional diffusion models based on weighted empirical risk minimization over both target and source domains. We establish the convergence rate of DA-Diff and show how transferable source data can improve target-domain estimation through an increased effective sample size while controlling transfer bias. Building on DA-Diff, we further propose Domain-Adapted Conditional Independence Testing (DA-CIT) and show that its Type I error satisfies $P(p \leq α) \leq α+ o(1)$. Experiments demonstrate that DA-Diff improved conditional generation quality compared with transfer-learning diffusion baselines, while DA-CIT provides strong Type I error control and competitive power.

Diffusion Transformers (DiTs) have established themselves as a scalable backbone for high-fidelity image synthesis. However, unlike U-Net based diffusion models that rely on rigid, hand-crafted skip connections, DiTs predominantly use a uniform residual stream that integrates all preceding layers as a monolithic state. In this work, we rethink residual connections in diffusion transformers and propose to transform them from passive summation into an active retrieval mechanism optimized for image denoising. First, we conduct a systematic analysis of DiT's internal representation, revealing a latent preference for early-layer feature reuse and symmetric layer guidance. Motivated by this, we introduce a structured connectivity design that explicitly integrates local residual connections with long-range pathways. Instead of static skip connections or dense all-layer routing, our method enables each transformer block to selectively ``attend'' to critical earlier representations, dynamically retrieving spatial and semantic cues through direct, differentiable cross-depth paths. Experiments show that our adaptive connectivity leads to faster convergence, with up to $1.73\times$ fewer training iterations, and significant gains in FID and visual quality with less than $0.1%$ additional parameters, further improving a strong REPA-XL/2 model from $5.9$ to $4.34$ FID without guidance and reaching $1.39$ FID with classifier-free guidance. Our findings suggest that adaptive cross-layer connectivity is a critical yet underexplored factor in diffusion transformers, and that incorporating structured information pathways provides a simple and effective direction for improving scalable generative models.

Most continuous diffusion language models process one latent position per token at each sampling step, making generation expensive. Two-stage methods lower the cost by reducing the latent length, but they fix the compressed embedding space before training the diffusion model. Embeddings from the fixed space can be difficult to model with diffusion and decode reliably into tokens, which limits generation quality after compression. To address this problem, we introduce JPEG-DLM (Joint-embedding Prediction for Efficient Generation with Diffusion Language Model), which jointly trains a compressor, a flow matching model and a decoding module. With joint-embedding prediction, JPEG-DLM learns compressed embeddings that are more structured, easier to model with diffusion and reliably decodable into tokens. JPEG-DLM achieves the lowest mean Gen-PPL and highest throughput among recent diffusion and flow models on LM1B and OWT. At a compression rate of 0.5 on OWT, it reaches a Gen-PPL of 34.52 and approximately 2.3 times ELF's throughput. These results suggest that jointly learning compressed embeddings offers a promising path toward efficient diffusion language modeling. Code will be released soon.

Post-training quantization (PTQ) is the standard way to run modern diffusion models on memory-constrained accelerators, yet every existing diffusion PTQ scheme fixes the $\mathit{number\ format}$ in advance and only tunes the scale, zero point, or per-layer bit-width. At a fixed bit-width the best format depends on the distribution being encoded, and that distribution differs across weight channels, across layers, and along the diffusion timestep, where activation distributions slide from heavy-tailed and noise-dominated to tightly clustered and structured. We propose Chameleon, a PTQ framework that holds the bit-width fixed and treats the format itself as a discrete variable, chosen per weight channel and per (layer, timestep bucket) activation tensor. Activation formats come from {INT8, FP8 E4M3, FP8 E5M2, MXFP8, MXINT8}, selected ahead of time from two cheap statistics (empirical kurtosis and the closed-form diffusion SNR) and stored in a lookup table; weight formats come from {INT8, MXINT8} at 8 bits or {INT4, NF4, FP4 E2M1, MXINT4, MXFP4} at 4 bits, selected offline by reconstruction error. An architectural fork adapts the same selection layer to multi-step UNets, single-step distilled models, and Diffusion Transformers. Across SDXL, SDXL-Turbo, and PixArt-$α$ on COCO-2014, Chameleon achieves the best FID in all six backbone $\times$ bit-width settings, with CLIP within 0.24 of the FP16 reference and the best of all quantized methods at $W_{4}A_{8}$.

ELBO-based reinforcement learning offers a sampler-agnostic approach to fine-tuning flow matching models with reward feedback. Timestep weighting in ELBO-based RL has large impact on performance, and it also provides a unified view (as we show in this work) to understand prediction losses heuristically chosen in prior work, yet it remains under-researched and is often chosen to inherit pretrain configs. We investigate impacts and dynamics of timestep weighting in ELBO-based RL. We show that effective weighting depends on both the reward landscape and stage of learning. (1) Through experiments on controlled CIFAR image generation, complemented by robotics, we investigate how weighting impacts reward-driven updates across noise levels. (2) Through gradient analysis, we reveal distinct patterns of cross-noise coordination across tasks and their evolution during training. These findings motivate the hypothesis that useful weighting depends on the gap between the policy's current behavior and the behavior favored by the reward. (3) Guided by this analysis, we study simple static weighting, budgeted profile selection, and dynamic schedules that improve performance beyond conventional target choices. Our results establish timestep weighting as an important design choice for flow-matching RL and motivate further research into methods that choose and adapt it throughout learning.

Reinforcement Learning (RL) has proven effective in aligning flow-based generative models with human preferences. Recently, Flow-GRPO has emerged as an efficient critic-free paradigm by calculating advantages over sampled candidate trajectories. However, standard Flow-GRPO applies a uniform scalar advantage across both temporal denoising steps and spatial latent dimensions, without explicitly accounting for the spatial structure of generated images, which may lead to sub-optimal policy updates. To address this, we propose a novel gradient-guided spatial credit assignment framework tailored for Diffusion Transformers (DiTs). We first reformulate the transition-level log-likelihood in Flow-GRPO into a token-wise representation natively aligned with DiT patch architectures, constructing spatially fine-grained importance sampling ratios. To allocate localized credit without rigid, boundary-sensitive segmentation heuristics, we introduce a continuous spatial credit map derived from reward gradients. Crucially, we employ an outlier-robust normalization scheme based on Median Absolute Deviation (MAD) coupled with temperature scaling, effectively eliminating gradient noise while highlighting functional prompt-aligned regions. Extensive evaluations on GenEval show that our approach delivers SOTA alignment quality, achieving a convergence rate comparable to top-tier methods like DiffusionNFT while substantially improving upon Flow-GRPO-based methods in alignment performance.

Diffusion models achieve state-of-the-art results across multiple tasks. However, in inverse problems, standard initialization from pure Gaussian noise misaligns the generative process with real-world degradations. More recent methods such as diffusion bridges impose strict endpoint constraints and often require long reverse processes that are prone to hallucinations. Alternative consistency models provide noise-invariant, one-step mappings but lack inherent variance modeling and can degrade under severe corruption. Hence, residual diffusion implicit models (RDIMs) are proposed, constituting a generalized framework that explicitly models the residuals between high-quality (HQ) and low-quality (LQ) images, aligning the forward process with the actual degradation. A non-Markovian implicit reverse sampler is derived, which can skip intermediate timesteps, enabling accurate few-step or even single-step reconstruction, while mitigating the hallucinations inherent to long diffusion chains. RDIM also introduces a controllable variance mechanism that interpolates between deterministic and stochastic sampling, balancing fidelity and diversity. Furthermore, it enables the straightforward use of perceptual losses, when needed. Experiments on denoising and super-resolution benchmarks demonstrate that RDIMs consistently outperforms the state of the art, including bridge and consistency models, in terms of PSNR, SSIM, and LPIPS, reducing hallucinations while requiring only a few sampling steps (often just one). The results position RDIMs as an efficient solution for a broad range of image restoration tasks.

Drifting models enable one-step generation by amortizing distribution transport into training, but this efficiency places greater demands on the transport field estimated at each update. In large-scale training, the field is computed from finite mini-batches of generated and real samples, which provide only imperfect approximations to the underlying distributions. Balanced optimal transport enforces exact mass matching within every mini-batch, making the estimated field sensitive to the particular composition of the real-data batch. We find that generated and real samples should be treated asymmetrically: letting the mass assigned to real samples adapt while keeping every generated sample fully transported improves generation across six feature-space metrics in controlled ablations, and is more robust to the relaxation strength than relaxing both marginals simultaneously, which falls below balanced transport under stronger relaxation. Motivated by this observation, we propose Unbalanced Optimal Transport Gradient Flow (UOT-GF), which keeps the generated-sample marginal fixed and relaxes only the real-data marginal. Under identical settings at DiT-B/2 on ImageNet-256, UOT-GF improves Fréchet Inception Distance (FID) from 1.53 to 1.46 over the balanced W-Flow baseline; scaling the same recipe yields 1.34 and 1.22 FID at L/2 and XL/2, the best FID among the one-step models we compare. We further derive the induced UOT transport force, establish a kinetic Vlasov--Fokker--Planck formulation whose overdamped zero-temperature limit recovers the drifting dynamics, and characterize non-target stationary states together with sufficient conditions for convergence.

Acquiring data is costly: higher measurement fidelity costs power and storage and risks collecting irrelevant content, while aggressive cost reduction can discard information that later analysis needs. We address this trade-off with an information-theoretic framework that acquires data relevant to a broad set of tasks rather than to one model. A mask policy, conditioned on side information, chooses which pixels to measure so as to maximize the mutual information between a discrete image and its partial observation under a budget; since the image entropy does not depend on the mask, this is equivalent to minimizing the conditional entropy. A frozen discrete denoising diffusion model (D3PM) supplies the posterior, and we use it in two ways: as an entropy surrogate for training a one-shot mask generator, and as the criterion for sequential greedy acquisition. The one-shot generator outperforms random masks only with care, including an unbiased gradient estimator for binary masks. With sequential acquisition, on MNIST the prior makes $8\times$ fewer errors than random at a $10%$ budget, and on CIFAR-10 it gains $0.9$--$3.4$~dB. On fastMRI, our proposed technique using a static mask outperforms the well-known methods such as variable density and LOUPE.

Data unlearning in diffusion models aims to remove the influence of specific training examples without suppressing the broader concepts they represent. However, when deletion requests arrive sequentially, updates for new requests can degrade generative utility and undermine earlier deletions. We propose a continual data unlearning framework that uses completed deletion transitions as directional references to regularize future updates. For each request, we record changes in denoiser responses on the same fixed noisy inputs before and after unlearning. Rather than matching full post-deletion responses, we apply a one-sided penalty that discourages reversal along the recorded directions relative to the post-deletion references, while leaving orthogonal response changes and progress beyond these references unpenalized. To keep storage independent of the number of requests, we maintain a fixed-capacity bank of representative transition records. Records are selected based on the local sensitivity of progress along their recorded directions to parameter updates, allowing them to be retained even when their penalties are inactive. Empirical evaluations show that the proposed framework achieves a better balance between deletion persistence and generative utility than existing unlearning baselines as requests accumulate, using only a small transition memory.

A trained neural network can be represented by a parameter vector in high dimensions. Learning distributions over these vectors enables the generation of new models across various tasks and architectures. A central challenge is permutation symmetry: permuting hidden neurons can produce distant parameter vectors representing the same function. This introduces variations that a generative model must account for when learning from trained networks. Existing methods typically address this using networks derived from a common base model or costly approximate neuron alignment. We instead parameterize a flow-matching velocity field with a permutation-equivariant Graph Meta Network, enabling direct learning from independently trained networks without alignment. Extensive experiments show that our method closely reproduces the joint statistics of accuracy, functional similarity, and weight similarity of independently trained collections, providing evidence of generation beyond checkpoint memorization. A single conditional model also generates task-specific networks on heterogeneous architectures and generalizes to unseen hidden-width configurations. On a tabular domain-shift task, intermediate conditioning produces individual networks with performance comparable to logit ensembles across both domains. Taken together, our results show how permutation equivariance enables learning from diverse collections of independently trained networks without permutation alignment.

Inferring quantities of interest (QoI) from data is a central task in Science and Engineering. In such contexts, we often have access to both quantitative data and qualitative data. Quantitative data may be represented by noisy sensor measurements, simulation data, re-analysis data; qualitative data may be in the form of text descriptions of experimental setups, expected experiment outcomes, and human-perceived system behaviours. The task we address in this paper is the following. Given a training set of paired qualitative text and quantitative QoI data, we learn to exploit the inherent correlation between the two modalities to learn a highly informative data-driven natural-language-conditional Bayesian prior, such that when presented with a new physical system, we can coherently combine (i) the training dataset, (ii) qualitative text describing the new system, and (iii) a small number of noisy sensor readings from that new system, to perform inference and uncertainty quantification (UQ) over the QoI. To achieve this task, we develop two parallel approaches, one uses conditional diffusion and the other conditional autoencoders, and compare both against classical Bayesian methodology, unconditional generative models and deterministic supervised methods. Each approach has specific strengths and tradeoffs; conditional autoencoder offers theoretical tractability, allows for fast posterior sampling, and provides better-calibrated UQ, whereas conditional diffusion is explored for greater expressiveness and capturing complex posteriors with irregular QoI fields. The approach is tested on the steady-state heat equation, damped Helmholtz equation, and UK weather reanalysis data.

Sampling-based motion planners guided by diffusion models produce high-quality trajectories in a single run, yet the stochastic diversity available at inference time is left largely unexploited. We present two inference-time diversification strategies for a fixed, pretrained DiTree model, combined via H-Graph hybridization, and evaluate them on a holonomic AntMaze robot across 15 maze scenarios. The first, factorial diversity, sweeps the random seed and Diffusion Goal Bias (DGB) parameter, the second, refinement-only diversity, sweeps the diffusion refinement strength (RS) that controls how much an RRT-generated trajectory is edited. Because a single-run baseline only partially succeeds, we additionally compare H-Graph results with pool-based statistics. H-Graph improves the mean pool length of the factorial and refinement-only diversities by 18.8% and 14.5%, respectively. In addition, it also improves the best individual candidate's lengths by 9.7% and 6.8%, respectively. And last, compared with the successful baseline's trajectory length, it improves the results by 18.2% and 19.9%, respectively. These results show that inference-time parameter variation is a reliable, training-free source of path diversity, and that H-Graph hybridization reliably converts this diversity into shorter, higher quality trajectories.

Efficient sampling from Boltzmann distributions is central to modelling complex physical systems. Markov Chain Monte Carlo (MCMC) methods suffer from critical slowing down, high autocorrelation, and poor mode-mixing, limiting their scalability. Recent advances, like Boltzmann Generators, offer a promising alternative but remain constrained by costly MCMC-based training, inefficient sampling, and poor ergodicity. We introduce an algorithm for learning Boltzmann distributions that does not require any true samples for training. Our approach draws inspiration from flow matching but departs fundamentally from sample-trajectory matching to distribution-trajectory matching. The algorithm iteratively reshapes the target distribution, using model generated samples to guide learning and ensure comprehensive mode coverage. We validate our method on standard benchmarks, including a 2D Gaussian mixture, Many-Well distributions, and high-dimensional scalar $φ^4$ theory. The proposed approach not only improves sampling performance and accuracy over traditional MCMC and flow-based baselines but also establishes a new method for sample-free learning of complex physical distributions.

We propose sliced Orlicz-Wasserstein (SOW) distance which is a generalization of sliced Wasserstein (SW) distance. SOW replaces the $L^p$ norm in SW with a Luxemburg norm cost induced by an Orlicz function $φ$. First, we prove that SOW distance is a metric on the space of measures with finite Orlicz norm, and show that it recovers the SW distance when the Orlicz function is $φ(x)=x^p$. Next, we derive the topological properties of the SOW distance. In particular, we show that convergence under SOW implies weak convergence, and the converse is true under the compact support condition. We then present the theoretical results for estimating the SOW distance. We derive sample complexity for both the distance itself and the powered functional of the distance, and prove their minimax optimality. In addition, we discuss the computational algorithm for approximating the SOW distance by Monte-Carlo estimation and bisection search, as well as the associated approximation error and computational complexity analysis. Our experimental results reveal the superior computational efficiency of SOW compared with Orlicz-Wasserstein (OW) distance. Also, in the experiments, we demonstrate the favorable flexibility of SOW distance over SW in detecting differences between distributions by comparing their performance in two-sample tests and evaluating generative models on image datasets.

Camera pose estimation from multi-view images remains a challenge in computer vision. Traditional methods often address this problem using Structure-from-Motion (SfM) with bundle adjustment. However, camera poses estimated from sparse views are inherently ambiguous due to insufficient geometric constraints. Recent work leverages probabilistic models, such as diffusion models, to generate multiple camera pose hypotheses and therefore capture this uncertainty better. Most of these methods represent camera rotations using unit quaternions, but treat them as unconstrained 4D vectors during the generative processes, thereby ignoring the unit-norm constraint of quaternions. Unconstrained quaternions create non-smooth and suboptimal generation trajectories. To this end, we propose *QuacamFM*, a quaternion-constrained flow matching framework for camera pose estimation that preserves unit quaternion representations throughout the entire flow trajectory. We design the optimal transport of the quaternion flows using smooth spherical linear interpolation. Experiments on CO3Dv2 demonstrate our method's advantage in camera pose accuracy over diffusion-based methods and classical SfM approaches. We further show that our quaternion-constrained formulation outperforms the naive application of standard flow matching to 4D quaternion vectors on sparse-view camera pose estimation. Finally, it is observed that QuacamFM generalizes well across datasets and in-the-wild examples.

Graph reconstruction from partial observations often comes with structural side information, such as degree bounds, triangle counts, or an edge-density band. Prior-Informed Flow Matching (PIFM) reconstructs graphs by transporting a local prior toward the graph distribution, but it provides no mechanism to incorporate this side information. We put forth Constrained Primal-Dual PIFM (CPD-PIFM), which augments the sampler with Lagrange multipliers that evolve along each trajectory. The multipliers respond to constraint violations at a predicted endpoint and guide subsequent sampling steps without retraining. We prove that the sampler inherits PIFM's permutation equivariance and bound its expected terminal slack by a term that decays as the inverse square root of the number of steps, plus two approximation terms. On three link-prediction benchmarks and nine combinations of datasets and constraints, CPD-PIFM raises feasibility by 11-26 percentage points and remains competitive with fixed guidance without selecting a separate multiplier for each constraint.

Diffusion language models (dLLMs) predict masked positions in arbitrary order, but their exact constrained decoders still encode constraints as sequential languages, whose state must track every unresolved dependency between positions. For relational constraints this encoding grows exponentially: for same-order copy, every finite automaton needs $4^k$ states, deterministic or nondeterministic, and every context-free grammar has size $2^{Ω(k)}$, while the factor graph of the same relation has size $O(k)$ and a 16-entry peak table. We introduce FactorDLM, a training-free decoder that represents finite-domain relations as a factor graph and, at each denoising step, conditions the model's mean-field prediction on that graph exactly by variable elimination. Decoding cost then grows exponentially with the induced width of the constraint graph, which replaces automaton size as the governing parameter. Because a finite automaton is a chain-shaped factor graph, one compiler enforces syntax and nonlocal relations together: on JSON records with cross-field references, a schema automaton alone leaves references dangling, relational factors alone produce malformed JSON, and the combined plan is valid on both counts, including on records of variable length. Across nine relational benchmarks and three backbones, every output satisfies every declared constraint at 0.4-6.9% projection overhead, where unconstrained decoding is 0-79% valid, and compiled projection answers repeated queries 13.6x faster than CP-SAT with eight parallel workers. Because model-free rules solve three of five standard benchmarks, we construct benchmarks with exact chance and fixed-template floors, on which selecting among exact constrained samples beats greedy projection. Which encoding is cheaper, sequential state or direct factors, depends on the constraint and is computable before decoding begins.

Scientific measurements such as single-cell RNA (scRNA) sequencing often take the form of nonnegative integer counts, whereas continuous-state diffusion models approximate this discrete structure using continuous coordinates. Building on stochastic chemical reaction networks (CRNs), a class of count-native Markov jump processes, we introduce CRNDiff, a structured framework that combines count-space diffusion with inference-time conditioning on rare subpopulations. An independent birth--death instantiation yields a closed-form transition kernel for forward noising. This kernel enables reverse sampling via forward-filtering backward-sampling (FFBS) and supports data-driven selection of the terminal noising time, eliminating the need for a validation sweep. This tractability also lets us introduce tilted Feynman--Kac (FK) steering, a method for sampling target subpopulations from a frozen generator without retraining. By tilting posterior marginals before FK particle correction, steering mitigates importance-weight concentration when the target population is rare. Using scRNA-seq data from the human heart cell atlas, we test the ability of CRNDiff to generate cell-type-specific distributions. Across the three evaluated target populations, CRNDiff achieves the highest conditional fidelity among the evaluated generative models, with larger mean purity margins for rarer target populations. Generated cells preserve marker-level differential-expression structure. Replacing real training cells for the target classes with generated cells yields downstream classification performance approaching that of the real-data reference.

Large video diffusion models offer expressive priors for embodied prediction and learning, yet their many-step sampling remains costly for interactive downstream use. Distribution Matching Distillation (DMD) enables few-step video generation, but can suppress robot--object motion while preserving visual quality. Examining DMD's teacher and fake-score signals, we find that weak re-noising keeps the teacher posterior concentrated near motion-deficient rollouts, limiting motion-restoring guidance. Meanwhile, stronger-motion rollouts tend to incur larger fake-score fitting errors, which can hinder the generator's learning of interaction dynamics. We propose DyMD, a DMD framework that adapts both teacher supervision and critic fitting to the evolving student. Temporal affinity--conditioned re-noise sampling adapts the timestep distribution to each rollout's current interaction fidelity by mixing the base schedule with a teacher prior motivated by local posterior variation, thereby balancing motion recovery and appearance refinement. To better track stronger-motion rollouts, dynamics-guided fake-score tracking uses a noise-conditioned predictor to estimate noise-relative fitting difficulty from latent temporal dynamics, then upweights predicted-hard rollouts in the critic loss. Using DyMD, we distill a 14B teacher into a four-step 1.3B student with no auxiliary modules at inference. On embodied-video benchmarks, the student improves R-Bench task adherence by $9.6$ percentage points and PAI-Bench-G Domain score by $5.1$ points over Base DMD while maintaining comparable visual quality. As a backbone for downstream action planning, our student achieves 34% mean success across two WorldArena tasks, compared with 16% for Base DMD.

Achieving precise control over multiple properties without sacrificing chemical validity remains a central challenge in molecular inverse design. Existing reinforcement learning (RL) methods fine-tune graph diffusion models by treating **reverse** sampling as a sequential policy, using a single terminal reward to optimize hundreds of coupled decisions. They often suffer from instability, validity collapse, and limited property gains. We introduce GraphFDM (Graph Forward Distribution Matching), a new online RL paradigm for graph diffusion that performs optimization through the **forward** process. GraphFDM uses valid generations to define a reward-tilted target distribution jointly optimized over graph size and molecular structure for each property condition, incorporating reinforcement signals into supervised learning without storing reverse trajectories. We derive the unique optimal target, prove a condition-wise improvement guarantee, and show that the fixed graph-size prior of standard graph diffusion leaves an irreducible matching gap. In multi-conditional polymer and small-molecule generation, GraphFDM achieves the lowest MAE on every target property, with reductions of up to 53.0% relative to the strongest baselines and chemical validity above 0.99. It further generalizes to out-of-distribution property combinations.

Reward-based diffusion fine-tuning faces practical challenges when desirable outcomes are rare or conditioning corrections are costly to estimate. In this work, we propose Diffusion Online $h$-guidance Fine-tuning (DOHF), which turns Doob's $h$-transform into a practical online training algorithm. DOHF assigns optimality weights to generated samples, estimates the normalized local correction $\nabla\log h$ under the current rollout policy, and distills it directly into the generative model. Theoretically, we characterize the population-optimal DiffusionNFT update as well as the various classfier free guidance methods through a unified $h$-transform perspective. Methodologically, our framework accommodates black-box and non-differentiable rewards without additional network evaluations. We further show improved alignments under three empirical scenarios. Our work demonstrates how adapting probabilistic conditioning through inexpensive estimation and iterative distillation can improve generative learning across statistical sampling and visual generation.

Generating independent, equilibrium samples of molecular systems at scale remains a central obstacle in computational statistical mechanics. Boltzmann Generators address this by pairing a generative model with importance sampling to obtain consistent samples from the target distribution. We introduce Normalizing Flow Flow Maps (NF$^2$M), which combines the strengths of recent stochastic flow maps with the tractability of classic normalizing flows to build a Boltzmann Generator. Unlike most methods, which correct the generative model only at the end, NF$^2$M reweighs each denoising transition as generation proceeds, avoiding wasted compute on trajectories that are ultimately discarded. At each denoising step, a conditional normalizing flow proposes clean configurations given the current noisy state (a simpler task than sampling directly from the target) and its exact likelihood enables correcting each proposal toward the true denoising transition of the target Boltzmann distribution. This is in contrast to most existing methods, whose likelihoods are approximate or expensive to evaluate, undermining the statistical reliability of the correction. We establish consistency of the corrected transitions and bound how approximation errors propagate through the sampling chain. We evaluate NF$^2$M on peptide systems, demonstrating improved sampling efficiency and sample quality.

While modern text-to-speech (TTS) systems generate highly natural speech and support inline non-verbal vocalization (NVV) tags, accurate control over these events remains challenging. A key gap is the lack of established post-training methods for non-verbal control in continuous autoregressive flow-matching TTS. To this end, we present NVAlign, a direct-gradient post-training framework for NVV tag-following in this architecture. We first perform supervised fine-tuning (SFT) of TTS models and an NVV-aware automatic speech recognition (NV-ASR) model on NVV-annotated speech, then freeze the NV-ASR model to serve as the reward model for post-training. A two-step gradient surrogate enables efficient reward backpropagation through the flow-matching sampler to jointly update the autoregressive backbone and acoustic flow head. Fidelity penalties and reference-velocity regularization help preserve speaker similarity and speech quality. Results from NVV-SuperBench and human listening evaluations show that NVAlign improves tag-following accuracy over SFT and Flow-GRPO baselines. These findings demonstrate that direct reward-gradient optimization can improve non-verbal control in continuous autoregressive flow-matching TTS. Audio samples are available at https://nvalign.github.io/.

Physical systems evolve continuously in time, yet their states are typically observed only at discrete times. Generating trajectories consistent with their probability densities from such observations therefore requires capturing the continuous-time evolution rather than only learning transition mappings between consecutive observations. We propose PhiBE-Flow, a framework that directly estimates the probability velocity field induced by the stochastic differential equation (SDE) which governs this continuous-time distributional evolution. PhiBE-Flow learns from discrete observations using a model-free approach requiring neither known SDE coefficients nor score estimation. We establish convergence guarantees for the method, accounting for both time-discretization and finite-sample errors. We evaluate PhiBE-Flow on systems of increasing complexity, from controlled stochastic numerical systems to Navier--Stokes dynamics and real-world videos. Our results show that PhiBE-Flow accurately recovers probability flows of stochastic dynamics, preserves multiscale physical statistics, and improves video generation performance over representative baselines. The code is available at https://github.com/R1fe/PhiBE-Flow.

Text-to-image diffusion models enable data-efficient "mimicry" attacks, wherein adversaries fine-tune the model on a handful of public photos to synthesize convincing forgeries of a target individual. A common countermeasure is to embed imperceptible, low-energy watermarks, yet recent studies show these signatures are brittle: modest post-processing or lightweight adversarial perturbations readily suppress detection, exposing a fundamental tension between imperceptibility and robustness. We introduce FeatMark, a watermarking framework that shifts from pixel-level, energy-starved perturbations to inconspicuous semantic features: small, scene-consistent micro-features that remain natural to humans while providing a stronger, machine-verifiable provenance signal. FeatMark builds domain-specific feature banks that encode each watermark as a compact concept program, pairing open-vocabulary semantic cues with reliable edit regions and instruction templates. It then automatically selects features that are both feasible and executable and injects them through modular, mask-guided concept editing, yielding highly localized, scene-consistent micro-edits that are difficult to perceive. We conduct extensive experiments across VGGFace2, CelebA-HQ, and WikiArt, evaluating against 10 strong watermark removal/purification attacks (including regeneration-style purification) and several bespoke adaptive attacks tailored to FeatMark, to assess perceptual fidelity, watermark detection accuracy, and robustness. We further demonstrate FeatMark's extensibility to video mimicry attacks. The results show FeatMark remains virtually impervious, withstanding all evaluated attacks with negligible bit-accuracy and fidelity degradation.

Most existing human motion generation (HMG) methods use cross-attention modules to inject text semantics, but ignore the importance of bidirectional modeling between motion and text tokens, which limits text comprehension. A straightforward idea is introducing multimodal diffusion transformers (MMDiT), which have shown effective joint text--visual modeling in vision generation, into HMG. However, we find that articulated motion is temporally coherent but weakly correlated across joints, in which directly applying an MMDiT with flow matching produces poorly coordinated and jerky motion. In this work, we propose Timo, a novel kinematics-aware MMDiT framework tailored for HMG. Timo combines fully shared multimodal attention for bidirectional text--motion modeling with flow matching, geometric and rotational-kinematics supervision that compares actual rotations and their changes over time, and a two-stage curriculum progressing from broad motion learning to detailed caption alignment. Further, we construct a benchmark of $40{,}025$ held-out clips from six public datasets spanning diverse actions, assessing six complementary dimensions under a common evaluator and scoring protocol. Our model substantially outperforms state-of-the-art methods in both quantitative and qualitative evaluations. Remarkably, Timo surpasses Kimodo on five of six dimensions, achieving a $40.8$% relative improvement in the average benchmark score. Project page: https://kyfafyd.wang/projects/timo. Demo page: https://timo.kyfafyd.wang.

Existing human motion diffusion methods provide strong motion generation quality, and recent style transfer models can inject target style cues, but fine-grained continuous control of style intensity remains underexplored. In production, style intensity is subjective across artists and directors, so the practical requirement is not a universal absolute unit, but a reliable monotonic control axis. We propose Motion Style Slider, a motion-to-motion style transfer framework for endpoint-supervised continuous control. Given a content motion and a style motion, we construct a style direction in a learned motion-style embedding space and condition diffusion generation with a scalar intensity. The training objective combines diffusion denoising with latent intensity regularization to encourage smooth and monotonic style scaling without requiring intermediate-intensity ground-truth motions. Our framework is compatible with pretrained motion diffusion backbones and supports heterogeneous style datasets, including the multi-actor style motion dataset. To test out-of-range usability, we additionally introduce a small real-capture over-reaction extension and evaluate large-intensity behavior against these unseen targets. Experiments measure controllability, interpolation/extrapolation behavior, content preservation, and motion realism, with ablations on direction construction and loss design.

Implicit neural representations (INRs) have gained momentum in scientific visualization due to their compactness and scalability to large datasets, making them well suited for integration with direct volume rendering (DVR). However, real-time volume rendering of INR with advanced illumination effects, such as shadows, remains computationally expensive, as evaluating shadow terms via ray marching is costly. Alternatively, precomputing and storing shadows for many lighting directions is prohibitive in both memory and storage. To address this, we introduce a diffusion-based shadow caching framework that compresses a vast set of pre-calculated shadow INRs into a single diffusion model. Rather than focusing on generalizing to unseen directions, our method effectively memorizes and reconstructs a dense set of pre-trained lighting conditions on the fly. We first encode a collection of shadow coefficient volumes as shadow INRs, and then train a diffusion model conditioned on lighting direction to predict the corresponding shadow INR weights at inference time. This design integrates directly with standard INR renderers without additional runtime sampling. Experiments show that our approach achieves faster rendering than traditional methods while bypassing the massive storage bloat of independent INRs, producing shadows that closely match most of the reference results.