生成模型理论与方法

Diffusion Transformers with Mixture-of-Experts (MoE) routing are a leading recipe for scaling generative models. Classifier-Free Guidance (CFG) is essential for generation quality, yet excessively high guidance scales trigger collapse. We identify a previously unreported failure mode in their combination: the two CFG branches route independently, so their realized activations occupy different subspaces. The unconditional write then leaves the conditional subspace, and CFG amplifies that residual linearly in the guidance scale. We propose SAGE, a training-time regularizer that aligns unconditional MoE activations to the conditional subspace without restricting routing diversity, at zero inference cost. Toy experiments show that SAGE dramatically suppresses extreme drift by 9.2x. When scaled to a 1B-parameter text-to-image model, SAGE significantly improves generation quality, delivering a 9.3% boost in peak DPG-Bench performance. Extensive experiments demonstrate that SAGE consistently outperforms the baseline.

Denoising Diffusion Probabilistic Models have shown remarkable performance in unconditional image generation. In order to generate images with desired semantics, recent works have restricted the solution space by using guidance constraints in the diffusion sampling process. However, for image enhancement across different domains, these methods struggle to balance two main requirements: looking realistic in the target domain (photorealistic images) and preserving relevant features of the source domain, e.g., low-quality renderings or art paintings. Here, small local changes can alter the fidelity of the image completely, while large changes in other regions might be insignificant. We introduce LocDiff, a locality-constrained guidance method for image enhancement, which serves as a zero-shot extension to pre-trained diffusion models, ensuring the preservation of critical features during domain adaptation. In this way, we retain important local features, while allowing less critical regions to remain unconstrained and not interfere with the guidance process for relevant regions. We evaluate our method on two different domain-shift tasks: For art-to-photo translation, we apply the method in a fully zero-shot setting, preserving facial identity from paintings while generating photorealistic details. For enhancing low-quality fetal ultrasound renderings, we demonstrate zero-shot inference with auxiliary prior alignment. Here, the objective is to artificially add high-resolution characteristics and produce photorealistic ultrasound renderings, a target domain for which no ground truth distribution exists. Our experimental results demonstrate that LocDiff achieves favorable realism-faithfulness trade-offs compared to state-of-the-art methods, enabling controllable cross-domain enhancement.

Conditional Flow Matching (CFM) models for text-to-speech (TTS) suffer from incoherent frequency evolution during inference. While similar spectral imbalances are addressed in diffusion models for other domains, those generic solutions fail to generalize to the inherently uncoordinated acoustic dynamics of CFM. We demonstrate that this issue can be effectively mitigated by introducing a novel training-free frequency-selective boosting strategy. Using the Discrete Wavelet Transform (DWT), our method dynamically modulates mel-spectrogram sub-bands during ODE integration, synchronizing spectral development by penalizing aggressive low-frequency growth and boosting lagging high-frequency details. Validated across diverse architectures (Matcha-TTS, F5-TTS, IndicF5), our approach reduces the required Number of Function Evaluations (NFE) from 32 to 26 and improves Frechet Audio Distance (FAD) by up to 61%, all without compromising mean opinion scores, speaker similarity, and speech intelligibility.

Neural Stochastic Differential Equations (Neural SDEs) provide flexible continuous-time generative models, but generic neural drift and diffusion networks are costly to simulate on long horizons and can give unstable gradients when the training signal is a path functional rather than a pointwise observation. We introduce SLiSDE, a family of Neural SDE models built from structured linear stochastic layers. Parallel-in-time simulation is obtained at the layer level, while expressivity is recovered by gated in-flow stacking: previous-layer paths modulate the next layer's latent flow through learned gates. For functional calibration tasks in which rare paths dominate the loss, we add an optional Girsanov tilt that acts as a learned importance sampler with an exact likelihood-ratio correction. We prove well-posedness, a discretisation error bound, validity of the change of measure, and a universality result: the terminal laws of the gated stack are dense in the space of square-integrable laws. Experiments on functional calibration benchmarks show that the structured model outperforms fully neural SDE baselines while retaining parallel-time simulation and stable importance weights.

Diffusion models have revolutionized generative modeling for continuous data through the gradual refinement of a belief state. This iterative refinement has not yet carried over to discrete diffusion models, which discard uncertainty at intermediate steps through categorical sampling (information collapse). We propose Simplex Diffusion Models (SDMs), a framework that lifts the diffusion process to the probability simplex to represent beliefs over categories. SDMs admit probability paths with closed-form reverse transitions and can be trained with a simple cross-entropy loss. Contrary to earlier proposals such as Dirichlet Flow Matching which requires integrating an ordinary differential equation, we introduce a DDIM-like sampler with a tunable level of stochasticity. Because SDMs operate on samples on the simplex, they can carry uncertainty across denoising steps, which mitigates information collapse. On OpenWebText, SDMs are competitive with strong Discrete Diffusion baselines, achieving $17.0$ GenPPL at $5.46$ unigram entropy in 64 sampling steps, close to real validation data. Even without Self-Conditioning (SC), SDMs outperform masked and uniform diffusion (with SC or predictor-corrector sampling) on code generation (TinyGSM, $T=0.1$; $49.0%$ vs. $45.8%$). Distilled down to 8 steps, SDMs solve $32.1%$ of GSM8K problems, more than distilled Discrete Diffusion models with 128 steps ($21.4%$).

Flow matching (FM) has recently emerged as a promising framework for generative modeling due to its conceptual simplicity and strong empirical performance. In FM, samples are transported along a vector field parameterized by a neural network, inducing a probability path that evolves from a simple noise distribution to the target data distribution, governed by an ordinary differential equation (ODE). However, existing FM approaches predominantly rely on probability paths derived from optimal transport (OT) between Gaussian distributions, which may be suboptimal for capturing complex data with inhomogeneous structures such as heavy tail or sharp contrast. In this work, we generalize FM to the broader class of location-scale families for handling data inhomogeneity and introduce a novel class of probability paths defined as geodesics on the manifold of probability distributions. We name this approach probabilistic geodesic flow matching to distinguish it from prior geodesic (Riemannian) FM methods defined in input space. We argue that Euclidean OT-based paths are not necessarily optimal in probability space and may limit modeling flexibility. Through synthetic benchmarks and scientific datasets at different scales, we demonstrate that the proposed method more effectively captures complex distributions, leading to improved or comparable performance compared with SOTA geometry-motivated generative models.

Tool agents use large language models to act through external tools, yet successfully executed calls can still leave user requests unfulfilled. Tool-agent repair seeks alternative call sequences that execute successfully and fulfill the original requests. However, repair requires exploring both operation choices and their concrete realizations, making complete-sequence regeneration costly. Moreover, regeneration repeats operation selection even when failure arises from how those operations are realized. The resulting challenge is to reduce this repetition while preserving exploration of alternative operations and realizations. Therefore, we formulate repair as hierarchical search over operation supports, which we introduce as sets of permitted operation types that define reusable search regions for concrete tool-call sequences. We propose ReCommit, a training-free, diffusion-guided framework for improving tool-agent failure recovery while reducing repair computation. ReCommit amortizes operation-level proposal computation across repair trials by reusing operation-type scores from a single parallel readout of a masked diffusion language model. These scores guide search across supports, while realization search explores alternative entity bindings, arguments, and action composition within each support. Experiments on real failures across four enterprise services in the Agent-Diff benchmark show 75.9% and 63.2% relative recovery gains with 61.3% and 51.3% reductions in mean full-budget repair time at repair budgets $B=3$ and $B=13$, respectively, over the strongest evaluated 8B comparison method. ReCommit achieves a favorable recovery--cost trade-off, including in comparisons with the evaluated 32B models.

Tool-based image editing (image retouching) is commonly formulated with autoregressive multimodal large language models (MLLMs) that sequentially generate reasoning, tool selections, and parameter values. In this work, we present a novel approach to tool-based image editing by framing the task as a flow matching problem. We introduce FlowTool, a framework that directly models the distribution of high-quality tool parameters conditioned on the input image and user instruction using conditional rectified flow. FlowTool combines a vision-language model backbone for multimodal understanding with a Diffusion Transformer parameter generator that transforms Gaussian noise into an editing plan. We train FlowTool with a two-stage supervised flow-matching curriculum, followed by reward-based post-training. Across MMArt-Bench, FlowTool-Eval, ArtEdit-Bench, and MIT-Adobe5K, FlowTool achieves significantly stronger reference-based performance than specialized MLLM editing agents and proprietary MLLMs, while remaining competitive with proprietary models under reference-free evaluation. Moreover, FlowTool significantly improves inference efficiency, reducing latency by at least $50\times$ while requiring nearly $2\times$ less memory than the compared baselines. These results demonstrate that tool-based image editing can be effectively modeled as conditional generation over structured continuous editing parameters, without autoregressive reasoning.

Discrete diffusion language models (dLLMs) expose a denoised solution at every step, which makes process reward model (PRM) guidance look like a way to spend compute at test time. We show that once denoising, PRM scoring, and outcome reward model (ORM) scoring are charged in the same budget of forward passes, its deterministic form loses to a much simpler baseline. Our PRMs score intermediate denoising states and are trained on the correctness of the final answer. On Dream-v0-Instruct-7B with 8 candidates per GSM8K problem, keeping the candidate with the highest PRM score at every scoring step reaches 65.18%, while independent sampling plus an ORM reranker trained for the task reaches 75.13%. The gap grows to 12.69 percentage points (pp) with 32 candidates, and is 9.85 pp on MATH and 12.16 pp on MBPP. We trace it to two separable failures. First, guidance prunes on a weak signal: on GSM8K, PRM ROC-AUC falls from 0.77 to 0.54 as the mask ratio rises, a decay that persists when states are relabeled with fresh rollouts, and pruning lowers the best accuracy reachable from the candidate pool from 81.05% for independent samples to 67.30%. Second, on GSM8K and MATH, the PRM is a poor final judge: a sequential Monte Carlo sampler at the same budget restores that ceiling to 77.89%, yet selecting with the PRM gives 65.48%, on par with deterministic guidance, while a PRM retrained on final states matches the ORM on identical candidates. MBPP separates the two: there the PRM reaches 65.47% when reranking finished programs, on par with the ORM, but 50.88% when it guides denoising. The results point to two targets for dLLM guidance: keep correct partial solutions alive through early denoising, and leave the final choice to a verifier trained on final states. We release the corpus of denoising states with outcome labels and evaluation toolkit for reproducible comparisons at matched compute.

Continuous diffusion generates complete reasoning solutions through iterative refinement in latent space. We introduce the Continuous Embedding Diffusion Reasoner (CEDR), an ELF-based training and inference recipe. Our experiments show that accurate decoding alone does not ensure strong reasoning performance. We therefore learn compact representations from multiple layers of a strong autoregressive teacher. Their decomposition also enables asynchronous denoising at different rates. We show that prompt encodings need only preserve the information required for the correct text-conditional score, rather than exactly match teacher features, and use a staged curriculum to learn a compact prompt encoder that replaces the teacher Transformer at inference. We adapt DiffusionNFT to learned self-conditioning guidance and incorporate gold-solution endpoints to supplement sparse rewards. Our supervised models outperform reported results from recent continuous-diffusion baselines at comparable backbone scales on mathematical reasoning and HumanEval code generation. With a 638M-parameter denoising backbone and learned prompt conditioning, post-NFT CEDR-L achieves 63.74% pass@1 on GSM8K and 24.6% on MATH500 at 64 denoising steps, and 32.85% on HumanEval and 30.18% on HumanEval+ at 128 denoising steps. Code will be available at: https://github.com/chengxiang/CEDR.

Diffusion language models (DLMs) can accelerate generation by predicting multiple tokens in parallel, but there is a mismatch between how these tokens are predicted and how they ultimately contribute to generation. Parallel predictions can hardly condition on the tokens selected earlier within the same block, even though their validity depends on this realized prefix. Under the popular proposal-verification decoding, this mismatch makes errors highly asymmetric: an early rejection prevents all subsequent proposals from contributing decoding progress. We introduce BRISK-DLM, a framework that addresses both mismatches by optimizing proposal learning and selection for verified progress. BRISK-DLM trains on self-generated sequences, using risk-reward weighting to dynamically prioritize positions by their impact on verified progress and decoding cost. During inference, a lightweight prefix-conditioned corrector reranks existing candidates using previously selected tokens and preferences distilled from the model's own verifier. The corrector reuses the backbone's parallel representations and requires no additional backbone evaluation, while fused execution keeps its overhead small. BRISK-DLM improves end-to-end throughput by up to 37.4% while preserving task quality, establishing a new quality-throughput frontier for DLM generation.

Precipitation nowcasting, generating future radar fields from past observations, is critical for flood warning and disaster response. It is also a demanding benchmark for spatiotemporal generative modeling, with chaotic dynamics, heavy-tailed intensities, and rare high-intensity structures that matter most. Deterministic models minimize a pixel loss and are driven toward the conditional mean, which blurs exactly those structures, while generative models that add a stochastic residual on top of a deterministic backbone inherit the same blur. We propose Physics-Guided Flow-Map Matching (PG-FMM), a conditional flow-map model that decouples predictable advection from uncertain small-scale detail. A frozen Lagrangian advection prior transports the radar field and supplies an explicit motion forecast, and a flow-map generative head, conditioned on the past frames and the prior rollout rather than summed onto it, produces sharp stochastic detail in four sampling steps. The prior serves only as guidance, so the head replaces blurred structure instead of inheriting it. Extensive experiments on four radar benchmarks show that PG-FMM outperforms state-of-the-art methods on 18 of 24 metrics, with the largest gains at heavy-rain thresholds, where the critical success index improves by up to 58.9%. The project page can be found at https://neurogica.github.io/PG-FMM.

Diffusion models are now widely used in Bayesian inverse problems in imaging as priors, where latent diffusion models are often used for larger scale problems to keep the computational complexity and model-size manageable. Unfortunately, the auto-encoder based compression results in loss of spatial detail. In addition, the optimization is converted to a non-linear problem. In this paper, we introduce a posterior sampling algorithm customized for the pyramidal/cascaded architecture, which relies on a coarse to fine hierarchical strategy to generate images in the pixel domain. We present CLIMB-Flow which alternates between three steps: an end-point estimation from the current coarse and noisy image, data-consistent update of the clean image, and re-noising it back to the level the network expects. Together these steps sample the posterior at that scale using an approximate Gibbs sampling from two conditional distributions. Experiments on ImageNet, CelebA, AFHQ and fastMRI span inpainting, deblurring, super-resolution and accelerated MRI, with PSNR gains of 1.37-7.66 dB over the strongest competing method on CelebA and pixel-domain reconstruction up to 512x512.

Masked diffusion language models (MDMs) admit flexible generation orders, making the unmasking strategy an inference decision. Existing methods vary in how they prioritize positions, control parallelism, restrict selection regions, revise predictions, or plan future denoising, yet it remains unclear when these choices should change during generation. We study this question through strategy reversals, where an alternative action becomes preferable to a fixed choice. We organize MDM inference into five axes--score, cardinality, region, commitment, and planning--and define adaptation opportunity as the one-step utility advantage of the best candidate action over a validation-selected fixed action. This view shows that adaptation value depends on both the frequency and magnitude of such reversals. Across three MDMs and ten tasks, adaptation opportunities are highly heterogeneous, with some regimes exhibiting concentrated and predictable one-step gains. This motivates selective adaptation: lightweight detectors calibrated on validation prompts identify high-opportunity states, capturing, for example, 56.9 percent of the candidate-set oracle opportunity by adapting only the top 10 percent of states on LLaDA-8B constrained JSON filling. Our transition-level results suggest that state adaptation is most useful when applied selectively rather than uniformly.

Diffusion large language models (dLLMs) generate text by iterative unmasking. At each denoising step, a dLLM proposes a token at every masked position, but the decoder commits only a confident subset of these proposals. Trace-based on-policy distillation (TOPD) builds on this process by matching the student to a stronger teacher, yet only at the committed positions. We argue that this discards much of the useful signal, which resides in the uncommitted proposals, where the student has made a prediction but is not yet confident enough to commit it. We call these proposals hesitations. In our pilot study on an SDAR-4B student, hesitations make up only 24% of supervisable state-position pairs but carry 66% of the teacher-student divergence. To exploit this signal, we propose Hesitation-Aware On-Policy Distillation (HOPD), which extends teacher distribution matching to every masked position of each denoising step. Because hesitations are not equally informative, we further allocate supervision using hindsight from the completed trajectory, placing more weight on positions whose proposal was later disagreed with the final token and on blocks where first-step proposals rarely survive. Since both models already produce distributions at all masked positions, HOPD requires no additional forward passes over TOPD. The only extra cost is evaluating the loss at more positions. With SDAR-1.7B and SDAR-4B students distilled from TraDo-8B-Instruct, HOPD achieves the best average score among the evaluated methods on five math and coding benchmarks, under both static and dynamic decoding and at both scales. It also speeds up decoding. On SDAR-4B, the HOPD student hesitates less and commits 11% more tokens per denoising step than TOPD, while reaching higher accuracy.

Guard models are the last line of defense between a language model and a harmful output, yet their training objective is surprisingly narrow. Existing guards learn to predict a single verdict token from a conversational context, concentrating supervision on a single target. The consequences are structural: models latch onto shortcut features, are overconfident, and remain sensitive to where safety evidence appears in the sequence rather than its role in the full context. We propose a different framing. Rather than predicting a label from text, our LLaDA-Guard asks which label better explains the text: scoring the prompt or response under each label hypothesis and classifying based on their difference. This shifts supervision to every token in the moderated region, forcing the model to account for full content rather than its most discriminative fragments. We instantiate this idea with a masked diffusion language model, fine-tuning LLaDA-8B-Instruct with a class-conditional reconstruction objective using LoRA and requiring no architectural changes beyond the base model. LLaDA-Guard leads on average rank against discriminative baselines trained on stronger backbones across seven held-out safety benchmarks, while exhibiting substantially better confidence calibration (ECE 0.0875 vs. 0.1384 for Qwen3Guard), less over-defense on benign prompts with unsafe-looking cues, and less prompt leakage when moderating responses. Its generative nature further enables token-level risk localization as a natural byproduct, yielding a pipeline for rewriting unsafe prompts into safe equivalents without additional training and achieving a 60.7% average conversion-to-safe rate.

We present VGGT-Diff, a geometry-routed multi-view diffusion model for sparse-view novel view synthesis. Existing novel view synthesis (NVS) methods face a fundamental trade-off: reconstruction-based approaches preserve observed geometry but struggle to synthesize unseen regions, while diffusion-based methods provide strong generative priors yet rely on implicit source-to-query correspondence. VGGT-Diff bridges these regimes by routing visual geometry latents from VGGT-Ω into a pretrained video diffusion model. Each visual token is associated with a 3D point and confidence, then transformed into query-aligned latent conditions through a confidence-aware Visual Geometry Router (VGR) that preserves front and back surface evidence. These conditions guide joint target-view denoising, while Point-Track Residual Consistency (PTRC) regularizes predicted-clean residuals along reliable 3D tracks, improving multi-view stability. We further introduce robust geometry conditioning, combining training-time regularization with inference-time guidance for improved robustness. Experiments show competitive or state-of-the-art performance across interpolation and extrapolation under different viewpoint difficulties. Our code is available at https://github.com/chenkangjie1123/VGGT-Diff.

Current grasp diffusion models provide rich priors for generation, yet their object-centric approach can violate the kinematic and collision constraints imposed by the embodiment and the environment. Existing embodiment-aware methods primarily perform local corrections around generated grasps through gradient guidance or optimization, making it difficult to recover from fundamentally infeasible modes. We present Steer2Grasp, a training-free, embodiment-agnostic framework for inference-time grasp steering that adapts a frozen Cartesian grasp diffusion model using deployment-specific rewards. Through Feynman-Kac (FK) inspired particle reweighting and resampling, the method reallocates population mass from infeasible to high-reward grasp modes, enabling population-level mode transitions without modifying the pretrained diffusion model or requiring differentiable constraints. The framework enables a unified treatment for single and dual arm grasping through reachability and collision aware rewards, followed by gradient free gripper level local refinement. Across diverse objects, robot embodiments, and constrained environments, our method substantially improves feasible grasp generation while maintaining proximity to the underlying grasp prior.

Concept erasure aims to suppress undesirable knowledge in text-to-image generative models. However, existing robustness evaluations typically rely on relearning attacks tailored to specific model architectures. We study concept reactivation across two substantially different generative paradigms: noise-prediction U-Nets and flow-matching Transformers. We introduce Concept Score Relearning (CSR), a unified parameter-level framework that reactivates erased concepts by optimizing each model within its native prediction space. CSR requires no external target-concept image dataset and applies the same concept-directed objective to both U-Net-based Stable Diffusion and Transformer-based FLUX. Experiments across diverse concepts and multiple erasure methods demonstrate consistent concept reactivation across both architectures, highlighting the cross-architecture applicability of CSR and the persistent recoverability of apparently erased concepts. For strict nudity, CSR reaches average ASRs of 50.47% on FLUX and 40.29% on Stable Diffusion, consistently ranking first across all evaluated safety settings.

Quantitative evaluation of generative models for radiology remains challenging. Clinically relevant structures are often small and infrequent, feature spaces learned from natural images may represent them poorly, and a single summary score cannot distinguish limited fidelity from limited diversity. This study proposes the Medical Multi-axis Maximum Mean Discrepancy score (M3-Score), an evaluation framework based on RadioDINO-s16, a frozen vision transformer pretrained on radiology images. M3-Score reports three complementary axes computed at pre-specified encoder depths: fidelity, measured by an unbiased multi-bandwidth radial basis function (RBF) MMD$^2$ at the final block; memorization, measured by nearest-neighbor distances at 75% depth; and coverage, defined as the fraction of real images with a generated neighbor within their $k$-nearest-neighbor radius at 33% depth. Reference sets are sampled across subjects to limit the influence of correlated slices. On BraTS brain MRI, the fidelity axis ordered five comparison sets of increasing severity (Spearman $ρ= 1.00$), and a subject-disjoint real set yielded $\mathrm{MMD}^2 = 0$ (permutation $p = 1$). An unconditional denoising diffusion probabilistic model achieved $\mathrm{MMD}^2 = 0.073$ (95% confidence interval $[0.071, 0.080]$) but covered only 38% of the real distribution. Under progressive mode dropping, $k$-NN manifold recall increased at all twelve encoder blocks, whereas the proposed coverage estimator decreased monotonically ($ρ= -1.00$). RadioDINO-s16 features separated real brain MRI from generated samples with a ROC-AUC of 0.819, compared with 0.555 for InceptionV3 and 0.582 for CLIP. Across a twentyfold range of sample sizes, the mean M3 value varied by a factor of 1.05, compared with 2.52 for the Fréchet Inception Distance.

As the bridge between protein modality and discrete modeling, protein structure tokenization still largely relies on heavily engineered training objectives tailored to specific downstream tasks and large training datasets, which hinders its transfer to broader application scenarios. To address this issue, we propose ProFiT, a lightweight flow matching tokenizer. With simple training strategies that encourage healthy codebook utilization, ProFiT can be trained efficiently and naturally learns semantically meaningful representations without any manual semantic alignment, while achieving reconstruction quality and generalization that match or surpass those of substantially larger tokenizers. We conduct extensive evaluations across a wide range of settings and demonstrate that ProFiT is a plug-and-play tokenizer adaptable to diverse downstream tasks. This study further reveals the significant potential of the flow matching tokenizer paradigm. Our code is publicly available at https://github.com/QDKStorm/ProFiT.

Sign Language Production (SLP) aims to generate sign motions from text. Conditional Flow Matching methods have achieved strong performance in SLP by constructing conditional paths that transform a source distribution into a target distribution. However, existing methods construct these paths via linear interpolation, whereas the rotational geometry of human joints confines valid joint rotations to a manifold embedded in Euclidean space. Consequently, linear interpolation between two sign motions leaves this manifold and ignores the motion distribution on it. In this paper, we revisit SLP from the perspective of manifold transport and propose a Naturalness-guided Manifold Flow Matching framework, termed SignNMFlow, which constructs conditional paths directly on the motion manifold by jointly considering geometric efficiency and the motion distribution. Specifically, we exploit the intrinsic geometry of the manifold and introduce a motion naturalness measure to characterize the motion distribution. By minimizing the kinetic energy under this measure, we learn a naturalness-guided interpolation that couples a closed-form geodesic, which provides geometrically efficient transport, with a learnable deviation that incorporates the motion distribution, thereby significantly improving the fidelity of generated sign motions. Extensive qualitative and quantitative evaluations demonstrate the effectiveness of this work.

Diffusion transformers incur substantial inference cost through repeated model evaluations along a sampling trajectory. We introduce GeoShrink, a training-free acceleration method that retains the original solver grid while evaluating the model only at a prescribed set of anchors. At skipped stages, GeoShrink predicts the solver-facing output by adding a geometrically retained fraction of the latest observed innovation to the most recent exact output. We derive this rule from chordal tangent transport and round-trip line projection, and establish a geometric anchor-spacing principle that minimizes the largest adjacent gap expansion under fixed coverage and first span. The analysis characterizes the geometric closure and propagation of prediction errors without assuming access to future model outputs. Experiments cover image, video, motion, and audio generation, together with adapted 3D backends. At approximately $5\times$ acceleration, GeoShrink improves FLUX PSNR by 3.10 dB over the strongest listed baseline. On HunyuanVideo, it achieves a reported $4.99\times$ speedup and improves ChronoMagic-Bench-150 PSNR by 5.44 dB over the strongest listed fidelity baseline. Comparisons at fixed evaluation budgets further show substantial gains on motion, audio, music, and 3D generation.

In dyadic human speaker-listener conversations, the listener's facial reactions allows the speaker to accurately perceive the listener's emotional states. Since human facial reactions are non-deterministic, the ability to generate multiple appropriate human-like facial reactions is crucial for realistic human-agent interactions. Although diffusion models are naturally suited to such one-to-many generation, existing diffusion-based Multiple Appropriate Facial Reaction Generation (MAFRG) methods attempt to denoise random Gaussian initialisations directly into multiple appropriate facial reactions (AFRs). These random initialisations are usually not well-aligned with the target listener facial reaction, which requires complex denoising trajectories from these initialisations, and subsequently creates substantial opportunities for deviations away from the range of trajectories leading to appropriate AFRs. Given the inherent mimicry between the human listener's and speaker's facial behaviours, we address the above denoising trajectory issue by leveraging this strong prior. Specifically, we propose ResDiffFRG, a novel diffusion-based MAFRG framework that explicitly anchors the diffusion process to the speaker behaviour by defining its diffusion target as the residual between the speaker anchor and an AFR. The denoiser only needs to model the comparatively small, reaction-specific residual needed to transform this anchor into an AFR, rather than reconstructing the complete reaction from an unstructured state. Extensive experiments show that ResDiffFRG achieves large improvements in correlation-based appropriateness over existing methods. Our denoising trajectory analysis showed that even at the start of the denoising trajectory, ResDiffFRG already achieves a higher facial-reaction correlation score than the Gaussian Diffusion baseline does after completing 60% of its denoising trajectory.

Repetition is closely associated with memorization in generative models, but how other training images affect the retention and copying of targets remains unclear. We study this question in class-conditioned flow matching, where images outside the target set form the background. At fixed target repetition and same-class background row count, replacing repeated same-class images with distinct images reduces the target extraction rate from 80.7% to 18.0%. To explain this effect, we develop a paired-trajectory framework that isolates target-induced parameter displacement and the background gradient response to it. This response has an exact path-integrated curvature representation, connecting background loss geometry to target learning. Reciprocal response transfer between repeated and distinct backgrounds changes target retention and copying in both directions, establishing the response's causal role. After target removal, the response correction parallel to the target-induced displacement preserves approximately 90% of the copying effects of full response transfer. Directly scaling the displacement also changes copying without further training. The post-removal copying effects of reciprocal transfer are reproduced across datasets and architectures. Together, these results identify the background gradient response as a mechanism through which same-class training data shape the retention of target learning and the reproduction of target images.

Generative models often suffer from mode collapse and limited sample diversity. While prior works attempt to mitigate this by jointly generating a batch of samples and repelling their trajectories, these heuristics do not explicitly maximize the diversity of the resulting endpoints. We introduce JIVE, a training-free framework that enhances generative diversity by injecting velocity perturbations aligned with the leading right singular subspace of the generator's endpoint Jacobian. By leveraging this local geometric structure, JIVE provably maximizes endpoint diversity while preserving sample quality. To maintain practical efficiency, we compute these perturbation directions via matrix-free iterations rooted in classical numerical linear algebra, requiring only a small computational overhead. Across different benchmarks, JIVE boosts both pixel and feature-level diversity in few-step and one-step generation.

Diffusion language models (DLMs) promise fast parallel generation, yet high-quality samples often require large number of refinement steps, which diminishes their advantage in practice. This has led to massive interest in and rapid development of new methods for effective few-step generation. We show that much of the supposed quality gap at few steps can instead arise from a suboptimally configured sampler. Modest sampler sharpening, without any model retraining, enables a couple years old masked DLM to rival supposedly far improved successors. This differently sampled DLM in fact achieves lower generative perplexity in just 16 steps than what its standard sampler obtains with 1024, while improving both judged quality and semantic diversity. We further show that conventional per-output metrics can fundamentally obscure these gains, since any optimal trade-off between two such metrics can be attained by a generator supported on at most two outputs. We subsequently introduce GroupEval, which separately evaluates quality and across-output semantic diversity, and offers fresh insights including uncovering how 1.5-4.7x perplexity gains of a distilled model yield no corresponding quality gain. Finally, we explain why sharpening helps: parallel unmasking destroys dependencies among simultaneously generated tokens, creating a gap between prediction and generation. We prove that pervasive temperature choice of one is generically suboptimal under parallel sampling even for an exact denoiser, and that worse predictions can yield better samples. Through these results, we argue for a broader evaluation principle of treating the deployed generator as the object of comparison, benchmarking it against tuned baselines, and assessing quality and diversity jointly and with more human-aligned measures.

Systematic out-of-distribution (OOD) generation remains a critical bottleneck for continuous-time generative models. While standard joint classifier-free guidance (CFG) routinely fails to synthesize unobserved concept combinations, exact decomposed scoring generalizes robustly at the cost of severe computational overhead. In this work, we reveal that compositional binding is not a uniform process but a highly localized phase transition. We identify the semantic bifurcation window - the precise temporal interval where joint and decomposed vector fields meaningfully diverge. Exploiting this dynamic, we propose surgical guidance, a hybrid sampling strategy that restricts exact multi-pass scoring strictly to this critical window. On an OOD bi-digit MNIST testbed, surgical guidance achieves state-of-the-art compositional fidelity at a fraction of the inference cost, yielding a +5.3% absolute improvement in pairwise accuracy over the joint baseline by intervening during just the first 15% of the diffusion trajectory. Furthermore, our empirical analysis uncovers a fundamental topological divide: diffusion models (SDEs) force conceptual resolution immediately at peak noise, whereas Conditional Flow Matching (ODEs) delays structural binding until intermediate features emerge, establishing a new temporal framework for accelerating large-scale generative decoding.

Deep generative models are used to solve partial differential equations and model distributions of physical system states, but ensuring that the generated samples satisfy the governing laws remains challenging. Projection-based flow-matching methods enforce physics by correcting the flow from an unconstrained noise distribution. These corrections shift the generated samples away from the distribution of target solutions, especially in high noise regions. To address this limitation, we propose Source Anchoring for Physical Consistency (SAPC), a Functional Flow Matching method that encodes the physical constraints into the source noise before generation begins. We evaluate SAPC on five systems governed by partial differential equations, covering six tasks with linear and non-linear dynamics, and compare results against five baselines and the unconstrained backbone. Anchoring the source reduces the need for large corrections that drive samples onto admissible but off-distribution states, and SAPC reproduces the target distributions most accurately on every evaluated task, while matching the constraint precision of the best projection-based baselines. Ablation experiments show that this gain arises from pairing source projection with a matched training objective that regresses toward the projected source. These results identify the source distribution as a key design choice for physically consistent generative modelling.

Learning population dynamics from temporally sparse, unpaired distribution snapshots is a fundamental challenge in developmental biology. Recent approaches based on neural differential equations and flow matching can interpolate between observed population snapshots, but may struggle to extrapolate beyond the training horizon and often lack an explicit mechanism for modeling developmental branching. We propose KoopCell, a unified generative framework based on Koopman-Mori-Zwanzig theory that jointly learns representations and predictive linear latent dynamics. Theoretically, using the weak continuity equation, we derive a closed-form least-squares estimator for the Koopman generator from distribution snapshots and establish convergence guarantees under suitable assumptions. To model branching dynamics, we further develop KoopCell-M, which incorporates non-Markovian memory into the latent Koopman dynamics through a Markovian embedding. Experiments on synthetic systems and three scRNA-seq datasets demonstrate the ability of our framework to recover Koopman spectra, model branching through memory, and scale to predicting high-dimensional gene expression distributions, achieving state-of-the-art performance among the evaluated methods.