生成模型理论与方法

Flow matching (FM) learns generative transport by fitting continuous-time motion from a simple source distribution to the data distribution. Most existing methods use first-order bridges: once a source and a target sample are paired, the path is a straight motion with constant velocity. FM with optimal transport (OT) improves the pairing, but the bridge itself remains linear, limiting its ability to model curved motion, acceleration, and changing directions. A natural remedy is to use second-order phase-space dynamics; however, learning the bridge requires target-side terminal-velocity information that static datasets do not provide. We propose Variational Terminal-Velocity Flow Matching (VTV-FM), a second-order FM framework that derives the missing velocity by minimizing acceleration energy, yielding a closed-form closure for static data. The same minimum-acceleration variational construction also defines the OT pairing cost and the acceleration targets used for training. Experiments on low-dimensional datasets, PDE-governed physical fields, and CIFAR-10 show that VTV-FM improves transport geometry and generation quality over first-order and high-order FM baselines.

Representation alignment has become an effective way to accelerate diffusion training, but its benefits do not transfer reliably to pixel-space clean-image prediction. In JiT, we find that auxiliary feature alignment can improve access to semantic features while reducing access to image variation needed for clean-image prediction, creating a mismatch between the auxiliary objective and the denoising task. This suggests a different principle: auxiliary supervision should improve the prediction target itself rather than impose a separate representation target. We introduce JAx (Just Align x), a prediction-supervision method that aligns clean-image predictions across noise levels. JAx couples a noisier student observation with a cleaner observation through a Markov degradation that preserves the original JiT input distribution. Under this coupling, the oracle prediction from the cleaner state has the same conditional mean as the optimal JiT target, while its conditional target covariance is no greater. Thus, oracle prediction alignment preserves the population JiT objective up to a constant while providing a lower-variance training target. To make this construction practical with an imperfect EMA teacher, JAx combines ground-truth supervision with a reliability-gated coupling band that selects nearby teacher states based on prediction risk. On ImageNet 256x256, JAx consistently improves FID and accelerates convergence across JiT-B/16, L/16, and H/16, without an external encoder or changes to the architecture or sampling procedure. Gradient diagnostics further show reduced minibatch gradient variance, while ablations demonstrate that the gains cannot be explained by time reweighting alone. These results show that prediction-space supervision provides a simple and principled alternative to representation alignment for pixel-space generative models.

Diffusion models with prompt and reference image-guided editing have seen rapid progress, yet they remain too coarse for pixel-level control. One promising direction is to incorporate a soft mask that specifies spatially varying edit strengths but training such fine-grained control demands expensive pixel-wise annotations, while existing zero-shot methods often yield unsatisfactory results. We introduce SoftPaint, a new zero-shot sampling method that leverages soft masks to enable a continuous spectrum of edits, from fully preserving the original content to completely re-synthesizing the masked region. Going beyond zero-shot inpainting methods, we design a Langevin-iteration-based sampler that respects per-pixel soft mask strengths, which applies universally to image and video diffusion models, enabling tasks such as video editing. The method is gradient-free, memory-efficient, and achieves smooth, pixel-level edits across multiple image and video backbones.

Inference-time steering enables pretrained diffusion models to satisfy new constraints without full retraining. However, specificity-aware generation is difficult: repelling samples from a negative reference distribution can also erode the positive distribution where the two overlap. The key challenge is to suppress negative mass while minimally distorting the positive distribution. We address this problem by formulating specificity-aware steering as a target-design problem and deriving a target distribution from an overlap-based objective. The resulting target keeps the desired reference distribution only in regions where it is sufficiently preferred over the undesired reference distribution, giving a likelihood-ratio interpretation of specificity. To sample from the corresponding time-dependent target path, we develop a Sequential Monte Carlo sampler with a variance-minimized local proposal. We further introduce a practical fixed-noise optimization procedure with the Jacobian--vector products with the desired and undesired score fields. Experiments on synthetic task, class-contrastive generation, text-to-image tasks and peptide-MHC (p-MHC) binder show that the proposed method suppresses undesired regions more effectively, reduces mode shift, and improves sampling stability by decreasing the SMC weight collapse compared with negative-guidance baselines. Code is available at: https://github.com/WangLuran/Specificity-Aware-Diffusion-Steering

Policy mirror descent (PMD) enjoys fast convergence in regularized Markov decision processes (MDPs), but existing guarantees often rely on exact or increasingly accurate policy evaluation. We analyze PMD coupled with a persistent critic advanced by one temporal-difference (TD) update. For finite discounted MDPs, we establish global linear convergence in value for exact coordinate-wise Bellman updates, with any positive constant actor stepsize and arbitrary finite critic initialization. The proof combines a resolvent-based auxiliary distribution with a decaying Bellman-violation correction and a potential weighted by inverse coordinate weights. We then study stochastic TD-PMD with general strongly convex mirror maps under a single off-policy Markov trajectory. With suitably chosen constant stepsizes and a finite-batch TD update, the method achieves an expected value gap of $ε$ after $\widetilde{O}(1/((1-γ)^5 \widetildeσ_b ε))$ transitions. The stochastic analysis relies on the trajectory-wise Lipschitz continuity of the regularizer, derived from uniform bounds on vertex Bregman divergences, together with a visitation-weighted resolvent estimate for signed critic-error propagation that yields an inverse-linear dependence on behavior coverage $\widetildeσ_b$. In contrast to many prior guarantees for regularized policy optimization, our sample-complexity guarantee holds without trajectory resets, generative-model access, or nested policy-evaluation loops. Numerical results are consistent with the theoretical convergence analysis.

Sampling several responses and voting over their answers can improve a language model's accuracy, but repeated answers limit the benefit of additional samples. Raising temperature increases diversity at a potential cost to per-sample accuracy. We introduce Self-Repulsion (SR), a sampler for masked diffusion language models that uses peer commitments to diversify the pool. At each penalized denoising step, each path lowers a token's logit according to how many peers have committed that token at the same position. Paths share a batched forward pass and then commit in sequence, so later paths observe choices made earlier in the same step. This coupling requires no training or additional forward or backward pass and can produce distinct paths even at temperature zero. When all paths commit a position together from identical logits, the update exactly maximizes total logit minus a convex duplication cost. On LLaDA-8B-Instruct with ten paths and 128 denoising steps, deterministic SR reaches 80.38% plurality accuracy on GSM8K, compared with 70.17% for the unpenalized greedy decoder. At temperature 0.6 and matched model-evaluation budgets, the count penalty improves over self-consistency by 2.06 percentage points in blocks of 32 and 14.50 under pure diffusion. Experiments on GSM8K, MATH and TruthfulQA show that voting gains arise mainly from higher coverage of correct answers, with gains that vary by benchmark and decoding regime.

Continuous diffusion language models generate all tokens in parallel, yet high-quality generation can still require hundreds of network evaluations (NFEs). We study how distributional distillation can reduce this cost by exploiting the student's probabilistic token outputs. Our unified formulation connects the student's output parameterization to the resulting gradient estimators and yields two methods with the same student architecture and reverse-KL matching objective: Simplex-DMD uses continuous token relaxations and pathwise gradients, while Reinforce-DMD uses categorical sampling and REINFORCE with a learned density ratio. We develop both methods for multi-step generation and investigate the training and sampling choices associated with each parameterization. On OpenWebText, for sequences of 1,024 tokens, Simplex-DMD achieves a generative perplexity of 45.6 at a unigram entropy of 5.44 nats in just 4 NFEs, a 49% reduction relative to the strongest evaluated diffusion baseline at matched entropy and sampling budget. Reinforce-DMD improves the frontier at larger budgets, reaching a generative perplexity of 14.9 at an entropy of 5.00 nats with 256 NFEs, a 20% reduction under the same comparison protocol.

Online reinforcement learning has been extended to flow matching for diffusion model (DM) image generation. However, this paradigm faces three limitations: (1) Window selection. Existing methods manually set the stochastic differential equation (SDE) sampling window, i.e., the denoising steps where exploration noise is injected. We instead determine it from each model's denoising trajectory. (2) Reward saturation. Current methods rely on scoring models trained on human annotations; we find that such scores are extremely high and nearly indistinguishable on the latest SOTA open-source DMs, making advantage estimation largely ineffective. (3) Sample inefficiency. A single scalar reward collapses different failure modes into almost identical scores, leaving minimal gradient guidance for targeted improvement. To address these issues, we propose CAST (Causal Advantage-Structured Training), an RL fine-tuning method for pretrained DMs, which (1) identifies the denoising step at which each model fixes the objects and their spatial arrangement in the image and uses that timing to set the SDE window, (2) decomposes each prompt via Causal Scene Graphs (CSG) into verifiable-atoms, i.e., minimal semantic units such as an object, count, attribute, or spatial relation that can each be checked independently, and rewards each atom separately, and (3) projects the signed atom-level advantages into pixel space through teacher-forced attention and uses them to spatially weight the SDE policy objective. We fine-tune two of the strongest open-source DMs, FLUX.2-dev and Qwen-Image-2512, with CAST, and evaluate them on GenEval 2, a compositional benchmark, and on Qwen-Image-Bench for overall quality. Within almost the same training budget, CAST's improvement over the base model on the most challenging GenEval 2 prompts is up to 3.07x that of Flow-GRPO, while overall generation quality also improves.

Text-to-image diffusion models are personalized to a subject by DreamBooth fine-tuning on a handful of its images. Increasingly, these images come from a diffusion model rather than a camera. We show that fine-tuning on such synthetic images degrades subject fidelity, producing oversaturated color and excess high-frequency detail. To isolate the cause, we fine-tune two models from the same base model with the same DreamBooth recipe, one on real photos of a subject and one on synthetic images of that subject generated by the first. We trace the degradation to classifier-free guidance (CFG). For the model personalized on synthetic images, the angle between the conditional and unconditional noise predictions, and with it the norm of their difference, is much larger than for the model personalized on real photos. This inflation grows toward high frequencies and also appears at other prompts semantically close to the subject, such as its class noun, but not at unrelated ones. We propose ReGain, a training-free correction applied at sampling time that measures how much each frequency band of the guidance is inflated relative to the base model and scales that band down accordingly. ReGain needs no real photos. On Stable Diffusion v1.5, ReGain closes 51-64% of the subject-fidelity gap to the model personalized on real photos, as measured by DINO, DINOv2 and CLIP-I. It also improves subject fidelity on SDXL and SD 3.5 and preserves text alignment on all three backbones.

Inference-time alignment of flow and diffusion-based models is critical for achieving flexible generative modeling. Theoretically, Doob's $h$-transform provides an elegant solution to this problem, and most existing methods are based on this principle. However, in practice, estimating the optimal guidance derived from Doob's $h$-transform at inference time is challenging. To deal with this issue, we regard inference-time alignment as a sequential optimization problem in the space of probability measures and propose a novel framework called *Steepest Guidance*, based on the principle of maximizing local improvement in the objective. We provide a theoretical analysis of the proposed method and demonstrate its effectiveness through extensive experiments.

Manifold-valued data, and consequently the distributions they induce, are prevalent across many domains, ranging from the locations of geospatial events, such as earthquakes, to biomolecular torsion angles that encode information about three-dimensional structure. While diffusion and flow-based generative models have been successfully extended to compact manifolds, sampling typically requires tens or hundreds of sequential network evaluations. We introduce RW-Flow, a theoretically grounded framework for learning one-step generative models on compact manifolds via Wasserstein gradient flows. The main challenge is identifiability: driving the velocity field to zero should guarantee that the model distribution matches the target distribution. We establish a necessary and sufficient condition for identifiability on compact, connected Riemannian manifolds. We specifically show that, for a symmetric, Lipschitz-continuous cost function, the velocity field induced by the Sinkhorn divergence is identifiable if and only if the associated Gibbs kernel is nondegenerate. This characterization provides a general principle for designing identifiable costs on compact manifolds. It also reveals that the squared geodesic distance, the natural manifold analogue of the squared Euclidean distance, does not always guarantee identifiability. Across benchmarks involving geospatial events, protein side chain torsion angles, RNA backbone torsion angles, and general manifolds discretized as triangular meshes, RW-Flow outperforms existing one-step methods in nearly all settings under fair comparison conditions.

We present PartiCam, a training-free Particle filtering rooted method for improved Camera controlled video generation. Generating videos that follow a precisely specified camera trajectory remains challenging for large video diffusion models. Training-free approaches are backbone-agnostic and avoid the need to construct large camera-annotated datasets by steering pretrained models toward the desired camera motion at test time. This enables the generation of camera-controlled video data that can subsequently be used to train camera-conditioned video diffusion models. Existing sampling-based guidance approaches often suffer from unstable trajectories: they either explore too broadly and fail to respect the target camera motion or collapse early and lose visual diversity over time. We introduce a global-local refinement framework for diffusion reward guidance, enabling accurate and consistent camera control during video generation. Our method builds on Sequential Monte-Carlo (SMC) guidance, but introduces a local refinement stage based on particle filtered resampling. Experiments show large improvements in camera trajectory adherence, reduced drift, and better visual quality, without requiring model retraining.

Although conventional world models - auto-regressive or diffusion models based on transformers or convolutional networks - may learn surface statistics of world dynamics, can they learn the exact world dynamics from its observed history? Leveraging cellular automata as a simple testbed, we find the answer to be no in many cases. Conventional architectures predict most pixels correctly yet rarely complete a rollout: a CNN predicts 96.3% of cells but completes 18.9% of rollouts; a joint diffusion model completes none. We trace the gap to three failure modes of these world models - namely, they fail to exactly capture spatial locality, temporal locality or temporal stability. Simple changes repair each: (1) for spatial locality, two-dimensional rotary positions lift a transformer from 39.1% to 100% on the Game of Life; (2) for temporal locality, handing each token its cell's previous-frame neighbourhood lifts the same transformer from 25.8% to 99.9% on unseen rules; (3) for temporal stability, causal freezing lifts the same diffusion weights from 42.2% to 99.9%. None of the three changes touches the architectural backbone; each only modifies the information flow within it. We also compare joint and ordered sampling on billiards and, in an exploratory study, on a simulated Burgers equation.

Multi-view learning seeks to learn more comprehensive representations by exploiting the complementarity and consistency across diverse modalities or views. However, existing multi-view fusion strategies treat intra- and inter-view fusion as independent stages, without simultaneously considering the evolution within views and the dependency across views. Such an asynchronous fusion paradigm inevitably constrains cross-view interactions due to conflicting view-specific structural inductive biases. As a result, information flow is prone to distortion and compression along intermediate pathways, confining the model to learn within a restricted solution space. To address this, we propose Synchronous Multi-view Neural Diffusion (SynMDiff), which conceptualizes the multi-view feature space as a unified dynamical system driven by a diffusion process. By modeling the diffusion flow across arbitrary dyadic feature interactions in a joint space, SynMDiff enables the concurrent and adaptive intra- and inter-view information fusion. While a direct implementation of this synchronized mechanism incurs prohibitive computational costs, we further introduce an energy-based topological sampling strategy and an Ego-Net style centralized training architecture, ensuring both efficiency and scalability during learning and inference. Due to its conceptual elegance and computational efficacy, evaluations on real-world datasets demonstrate that SynMDiff outperforms the baselines by a large margin.

Count data pose a challenge for score-matching-based causal discovery: derivatives are unavailable, and simply replacing them with finite differences does not generally suffice for causal discovery. We generalize SCORE's constant-curvature criterion (Rolland et al., 2022) by conditioning on the node's value, yielding the conditional curvature score (CCS) for ordering. We also extend curvature-based parent recovery through the off-diagonal curvature score (OCS), enabling directed acyclic graph (DAG) recovery with both scores constructed from score functions for continuous data and concrete scores for counts. In the bivariate setting, zero CCS exactly characterizes a semiparametric generalized linear model (GLM) conditional form in which the conditional family need not be specified in advance, unlike in classical GLMs. For bivariate semiparametric GLM DAGs under our regularity condition, canonical-parameter nonlinearity is necessary and sufficient for identifiability. In multivariate DAGs, this nonlinearity enables DAG recovery through CCS and OCS. Our framework identifies a new class of semiparametric GLM DAGs that strictly contains the nonlinear Gaussian ANM class identified by SCORE. We introduce DISCO (DIscrete SCOre), a count-DAG recovery algorithm that estimates CCS and OCS using discrete diffusion. Experiments demonstrate accurate DAG recovery across Poisson, negative binomial, binomial, and mixed-family settings, as well as scalability to 1,000-node DAGs on a single GPU.

Graph generative models increasingly rely on Graph Transformers (GT) to capture complex dependencies among nodes and edges. While deeper architectures should provide greater expressive capacity and a broader receptive field, their effectiveness can decline with depth: repeated self-attention progressively contracts node representations, impeding information flow and gradient propagation. We analyse this phenomenon from a dynamical systems perspective, focusing on how the denoiser's spectral dynamics affect graph generation. We show that standard GT denoisers become increasingly dissipative as depth grows, leading to vanishing gradients and representation collapse. To isolate the effect of these dynamics, we construct a permutation-equivariant GT with inherently stable, non-dissipative transport. We also introduce a damping mechanism that continuously interpolates between non-dissipative and increasingly contractive regimes, enabling a direct assessment of how dissipation influences generation. Experiments on synthetic and molecular graph generation benchmarks show that the gap between these regimes widens with depth: non-dissipative dynamics preserve representation diversity and gradient flow, sustaining strong generative performance, whereas greater contraction progressively impairs it. These findings identify the denoiser's dynamical regime as a key design factor for deep graph generative models.

Diffusion models are typically viewed as stochastic processes that transform noise into data. We take a complementary perspective: a diffusion model defines a family of deterministic dynamical systems indexed by noise scale. At each fixed scale $σ$, we treat the denoiser as a self-map and study its dynamics. For an exact denoiser, fixed points correspond to critical points of the smoothed data density, while attractors correspond to its modes; as $σ$ increases, sample-level modes merge into progressively coarser ones. This suggests a geometric view of memorization: examples that receive excess probability mass due to duplication or overfitting, as well as outliers, should remain distinguishable under stronger smoothing than ordinary examples. We quantify this persistence by the critical scale $σ_c$, the largest noise scale at which an example is retained by the fixed-scale dynamics. In conditional models, the same construction extends naturally to image--caption pairs. Experiments in controlled settings and on large-scale models show that $σ_c$ tracks memorization arising from duplication, overfitting, and outliers, and identifies both memorized and partially memorized examples in Stable Diffusion. Moreover, $σ_c$ yields interpretable measures of the image spatial distribution and caption dependence of memorization.

On-policy distillation (OPD) has demonstrated two important capabilities in language models: compressing large teachers into smaller students and merging expert models into a single model. Existing diffusion OPD, however, mostly focus on the latter, with teachers and students sharing the same backbone and scale. We investigate large-to-small diffusion opd from large teachers to a small student and find that the standard recipe fails. To find the underlying cause, we propose Fixed-State KL, an effective and fair way to measure the distribution gap between student and teacher during OPD training for diffusion models. We are the first to clarify why large-to-small OPD is challenging for diffusion models: a smaller student struggles to perfectly match the distribution of a larger teacher, while classifier-free guidance can accumulate and amplify the distributional discrepancies between the student's conditional and unconditional branches and those of the teacher. To solve this problem, we propose GFD-OPD, a simple yet effective method that reduces the student-teacher gap while avoiding the error amplification of the CFG composition. Across numerous experiments, GFD outperforms previous baselines in both training efficiency and final performance, achieving state-of-the-art results on all benchmarks.

We study the problem of estimating the guidance that steers the distribution learned by a diffusion generative model toward a tilted target $q_0 \propto w\,p_0$ at inference time. Relying on the stochastic optimal control approach, we observe that the exact drift correction is the gradient of the logarithm of Doob's $h$-function, and we study the problem of estimating it from a sample. In the present paper, we assume that the score of the pretrained model is available, that the tilting weight is bounded and positive, and that the reference distribution has a bounded support, no smoothness of the weight is required. Introducing a penalized least-squares risk in which the penalty is the residual of the space-time harmonicity equation satisfied by the $h$-function, measured in a dual Sobolev norm, we derive high-probability bounds on the squared error of the resulting guidance estimate. Since the penalty vanishes at the target, the estimator is free of regularization bias, and in favourable scenarios its rate of convergence is faster than the minimax rate of estimating first-order derivatives of a smooth regression function. Assuming that $w$ is bounded and positive with $\mathbb{E}_{p_0}[w^{-\mathrm{s}}] < \infty$ for some $\mathrm{s} \in (0,\infty]$, and that the reference data are compactly supported, we prove that the guidance is estimable in squared $L^2$ at rate $\varepsilon_n^{\mathrm{s}/(\mathrm{s}+4)}$, where $\varepsilon_n = n^{-2(β-1)/(2(β-1)+d)}.$ We also transfer the obtained bounds to the total variation distance between the marginals of the estimated and the exactly guided samplers, and illustrate the performance of the suggested approach with numerical experiments.

This paper proposes MIND, a marginal-invariant neural dependency diffusion model for mixed-type tabular data. MIND does not directly learn the joint distribution in the original heterogeneous feature space. Instead, it first maps different variable types into a unified latent dependency space via column-wise marginal transport. A conditional diffusion model then learns cross-column relationships. Copula-tangent denoising separates known marginal components from learnable dependency residuals. Rank projection during the sampling phase further mitigates marginal shift in reverse diffusion. Experiments across nine diverse tabular benchmarks show that MIND consistently improves marginal fidelity and dependency preservation over existing unified approaches. By explicitly isolating marginal modelling from dependency learning, MIND achieves a strong and stable balance among marginal fidelity, joint dependency preservation, and downstream prediction utility. This work supports separating marginal and dependency modelling as a principled and highly effective paradigm for complex mixed-type tabular generation.

Physics-constrained generative models aim to generate physical fields that match a target distribution and satisfy prescribed constraints. However, enforcing these constraints often increases sampling costs through iterative corrections or training costs through residual optimization and trajectory unrolling. To address this issue, we introduce Preconditioned Manifold one-step Flow Matching (PMosFM), a preconditioned manifold matching framework for one-step physics-constrained generation. By encoding constraints in a manifold decoder, PMosFM learns transport in intrinsic coordinates without separate residual losses or terminal residual unrolling. A geometric preconditioner rescales coordinates using the decoder-induced metric, while a regularized covariance transform approximately whitens the interpolation-state inputs. A finite-interval objective couples velocity supervision with consistency between decoded endpoints in physical space. We show that exact parameterization removes residual-induced Gauss--Newton curvature, that geometric and covariance effects separate in a local conditioning bound, and that physical flow-map error bounds endpoint distributional error. Controlled ablations examine conditioning, and experiments evaluate optimizer-update time and memory footprint. At inference, PMosFM uses one neural transport evaluation followed by physical decoding. Experiments across benchmarks show lower training and sampling time than the multi-step baselines at comparable physical and distributional fidelity. Code and datasets will be released publicly.

Training data attribution for diffusion models aims to identify the training samples that influence a generated instance, but existing methods either require costly per-sample gradient computation or query-specific model optimization. Moreover, most methods attribute changes in a proxy loss rather than changes in the actual model's generative behavior. We address these limitations by formulating attribution directly with a local score discrepancy measure, which applies to any diffusion variant (including DDPM, EDM, and flow matching), and by showing that such measure can be estimated without retraining, as a preconditioned gradient similarity. We instantiate this estimator as Training-data Influence via score Discrepancy (TID), which uses Kronecker-factored curvature to avoid random projections and per-sample gradient storage. We then distill TID into TIDE, a forward-only student trained online to reproduce the teacher's rankings from the diffusion model's internal activations. Under counterfactual evaluation on CIFAR-10, ArtBench-10, and MS-COCO, TID matches or outperforms state-of-the-art approaches, while TIDE retains most of TID's accuracy at four to five orders of magnitude lower per-query cost, attributing generated samples in milliseconds and faster than the generation itself.

Photospheric vector magnetic fields are foundational to modeling, understanding, and forecasting solar activity. These data are usually produced by inverting and disambiguating the full Stokes vector at multiple passbands, which is demanding. Here, we investigate how well we can estimate photospheric vector magnetograms from UV/EUV filtergrams. This problem is challenging and intrinsically ambiguous without polarization information, as the mapping from UV/EUV intensity to the magnetic field is indirect and ill-posed. We introduce MAGiDiff, a machine-learning-based method that uses denoising diffusion models to estimate vector magnetograms from UV/EUV filtergrams. As input, MAGiDiff takes a stack of filtergrams from the Solar Dynamics Observatory (SDO) / Atmospheric Imaging Assembly (AIA); as output, it is trained to estimate the disambiguated vector magnetogram as seen by Hinode / Solar Optical Telescope-Spectro-Polarimeter (SOT-SP). We show that MAGiDiff can accurately mimic the Hinode ground-truth. Additionally, we probe MAGiDiff's understanding of the physical structure and magnetic connectivity. On full-disk, we show that it produces plausible structures for active regions. MAGiDiff generalizes across solar cycles despite hemispheric polarity reversal, and can be fine-tuned to other EUV instruments including STEREO/EUVI and GOES-R/SUVI. While clearly not a substitute for a dedicated instrument, MAGiDiff opens the door to new capabilities.

Generative models for tabular data are typically trained separately for each dataset, limiting knowledge transfer and requiring the storage of many specialized models. In this paper, we introduce CDMD, a tabular diffusion model trained jointly across heterogeneous datasets with different schemas and variable numbers of numerical and categorical features. Unlike existing cross-dataset tabular diffusion models that operate in continuous representation spaces, CDMD defines diffusion directly over the mixed-type feature space and is trained end-to-end. To accommodate heterogeneous categorical domains, we introduce a schema-restricted reverse-process parameterization for masked diffusion models, in which the output space dynamically adapts to each feature's vocabulary. We then compose numerical and categorical feature-level diffusion processes into a schema-dependent row-level process. A shared schema-aware Transformer denoiser captures dependencies between features and parameterizes the reverse process across varying schemas. On seven real-world datasets, a single jointly trained CDMD achieves the highest average generation quality among strong single-dataset and cross-dataset baselines, while using substantially fewer total parameters than the collection of separately trained models. Furthermore, pre-training on a corpus of 337 datasets improves generation on previously unseen datasets under both limited target data and limited adaptation epochs. These results demonstrate the potential of direct mixed-type diffusion for shared and transferable tabular data generation. Our code is available at https://github.com/ketatam/cdmd.

Adapting a pretrained generative model to an arbitrary preference expressed as a utility function underlies reward alignment, guided design, and constraint satisfaction, enabling diverse applications. Existing fine-tuning methods trade off generality against computational cost: they either restrict the family class of supported preferences to keep optimization simple or preserve generality at the expense of efficiency. We introduce Fenchel Tilt Flow Control (FTFC), which decouples utility optimization from generative-model fitting. FTFC first optimizes for a target distribution by jointly fitting an effective reward and density-ratio weights on pretrained samples. Method combines the utility's variational structure with Fenchel duality, supporting general $f$-divergence penalties that determine how rewards are transformed into an distribution-correction weights. These weights are then frozen and used to modify a diffusion or flow model in a single stage of importance-weighted denoising or flow matching, without differentiating through sampling trajectories. We establish exact duality for concave utilities under suitable conditions and show that weighted fitting reproduces the optimal target distribution for a given utility. Across image and molecule generation benchmarks, FTFC improves over baselines on diverse preference functions, while also being up to $20\times$ more efficient. roposed method enables adaptation beyond expected-reward maximization without complex optimization, while preserving robustness for more general class of the utility functions compared to baselines.

Masked diffusion language models (dLLMs) have shown strong potential for faster inference through parallel token generation when combined with confidence-based samplers. However, recent work has shown that such methods can defer unmasking high-entropy fork positions at which multiple plausible continuations exist. This results in reduced generation diversity, as shown by worse pass@k scaling, and limits gains obtainable from RL post-training. To avoid this flexibility trap, prior work advocated for autoregressive (AR) sampling. Here, we show that discarding confidence-based sampling is unnecessary and, once inference cost is taken into account, wasteful. We first propose Fork-dLLM, a simple hybrid sampler that uses AR-style ordering only at uncertain fallback steps while retaining parallel generation otherwise. We then extend the same principle to post-training with ForkGRPO, which uses Fork-dLLM rollouts and applies the GRPO objective only at fallback steps, preserving exact policy-likelihood ratios while substantially reducing rollout and optimization cost. In our experiments, Fork-dLLM matches the strong pass@k scaling of AR sampling while being 2-3x more efficient, and ForkGRPO achieves downstream performance comparable to or better than AR-based GRPO baselines at a substantially lower training cost.

Diffusion distillation is widely adopted to accelerate sampling, and the resulting few-step models are broadly believed to match or even surpass their multi-step teachers in generation. However, standard evaluations such as GenEval2 typically draw only one sample per prompt, so improved scores may fail to reveal losses in distribution coverage. We therefore revisit whether distilled models truly match their teachers beyond single-draw performance using \textbf{pass@$\mathbf{k}$}, which measures the probability that at least one of $k$ independent samples satisfies a quality criterion. At $k{=}1$, pass@$k$ reduces to standard single-draw evaluation. As $k$ grows, the curve reveals whether additional draws find genuinely different successes or merely revisit the same modes, directly exposing how broadly a model covers the space of valid outputs. We first show that classifier-free guidance (CFG), whose quality--coverage tradeoff is well established, is the clearest case: higher guidance improves pass@$1$, but its advantage shrinks and reverses at larger $k$. Applying pass@$k$ to few-step distilled models, we find the same tradeoff splits along training objectives: distribution-matching objectives concentrate the student's output distribution, boosting early-hit rates while eroding large-budget coverage, whereas consistency and trajectory-based objectives better preserve the teacher's coverage even at large $k$. We further show that this tradeoff extends to few-step causal video generation. Our findings reveal a previously overlooked cost of diffusion distillation: across both image and video generation, the choice of training objective fundamentally determines whether a few-step model inherits its teacher's distribution coverage or trades it away for single-draw quality.

High-compression tokenizers are essential for scaling latent image generative models. However, aggressive compression creates a fundamental tradeoff between reconstruction fidelity and generation efficiency: high compression image encoder always increases the learning difficulty of diffusion training, resulting in slow model convergence. Recent representation autoencoders speed up the diffusion training by improving the latent feature's expressive capability by replacing VAE encoders with pretrained semantic encoders, yet they are typically limited to moderate compression and lose pixel-level details necessary for faithful reconstruction. To achieve both high compression and fast diffusion training, we propose DC-SAE, a Decoupled Compact Semantic Autoencoder designed for high-compression image generation with accelerated diffusion model convergence. DC-SAE consists of two key components: (1) a macro-level architecture design that leverages semantic encoders to enable higher compression ratios, and (2) a pixel-level encoder that preserves low-level details, ensuring high-fidelity image reconstruction. We empirically demonstrate that DC-SAE performs strongly on image generation tasks, achieving both compact latent representations and efficient training dynamics. Specifically, on the ImageNet dataset with $512 \times 512$ resolution, DC-SAE achieves $32\times$ spatial compression, with 29.79 PSNR and 3.37 gFID, substantially outperforming the previous state-of-the-art high-compression tokenizer baselines DC-AE by 13.5% and 54.9% on PSNR and gFID, respectively, maintaining comparable throughput and faster diffusion model training convergence. Beyond class-conditional generation, a $1.6$B-parameter DiT using DC-SAE achieves 0.84 on GenEval and 86.007 on DPG-Bench for text-to-image generation at $1024\times1024$ resolution.

Offline multi-objective optimization (MOO) seeks solutions with better objective trade-offs using only a fixed dataset, without querying the objectives. Diffusion models trained on such data have emerged as a promising approach, but their samples are not inherently better than the data and must be steered toward the Pareto front. Existing methods guide or condition every sampling step. We instead act on the initial noise and leave the sampling process unchanged. Across Off-MOO-Bench, we observe that the objectives, as functions of the noise, are sensitive to only a few directions. We estimate these directions once per task via a Recursive Feature Machine using function values alone, and a small cache serves every trade-off, so each candidate costs one noise displacement and one ODE solve. We prove that this displacement increases the learned scalarized objective in expectation, and that sweeping trade-offs recovers the flow's attainable front up to proxy and steering errors. With additional guidance, for which we introduce novel data-adaptive and Pareto-aware operators, our method attains the best average hypervolume rank among generative methods on 47 tasks, at comparable or lower sampling cost. Steering alone outranks the best prior generative method at a fraction of its sampling cost.

Diffusion models generate data by reversing a forward corruption process that typically approaches a simple Gaussian prior. Recent work has extended this framework to signals supported on fixed graphs, e.g., road-network traffic and sensor-network measurements. Many graph signals have nonuniform spectral energy, whereas isotropic corruption adds the same conditional noise variance to every graph-frequency mode. Driving all modes to near-zero terminal signal-to-noise ratio (SNR) requires strong corruption, which increases the noise range that must be covered under a fixed sampling budget. We introduce Graph Residual Conjugate Diffusion (GRCD), which replaces the shared clock of graph heat diffusion with a mode-dependent clock that gives every graph-Fourier mode the same conditional SNR. GRCD fits a zero-mean graph-spectral Gaussian reference on the training split and stops at a finite terminal SNR at which the propagated reference still carries the fitted spectral variances. The Gaussian component has an exact modewise propagator in the probability-flow ODE, so sampling advances it analytically and integrates only the learned residual score numerically. We evaluate GRCD on five settings (METR-LA traffic, Molene weather, and three stochastic block models) against seven comparators under a matched protocol: Graph-Aware Diffusion (GAD), EDM (graph backbone), two adaptations of Whitened Score Diffusion (WSD), and three preconditioning controls. At four function evaluations (NFEs), GRCD lowers averaged maximum mean discrepancy (aMMD) by 22 to 36 times over the best comparator on all five settings, reaching 0.054 on METR-LA, where it clears an aMMD 0.1 target with 87% less sampling wall-clock time than the cheapest comparator that reaches it. Fitting the terminal reference reduces aMMD by 2.7 to 7.3 times at finite terminal SNR, while the factors shrink to 1.00 to 1.01 near zero.