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This report presents MegaAvatar, a controllable talking avatar generation framework built on top of the Wan2.2-TI2V-5B model. Compared with previous talking-avatar methods that mainly rely on audio or reference-image conditioning, we introduce additional SMPL-X-derived 3D guidance, enabling global control over body pose and head motion. Specifically, we render the driving SMPL-X sequence into dense mesh frames and encode them with a lightweight 3D convolutional encoder, whose outputs are injected into the latent tokens to provide overall motion control. Furthermore, we extend Wan2.2-TI2V-5B with additional audio and face cross-attention modules to enable fine-grained expression control and preserve the input identity, respectively. In addition, we implement an audio-to-SMPL-X model to predict an SMPL-X sequence conditioned on the reference image and input audio, allowing MegaAvatar to support audio-driven inference without user-provided SMPL-X frames. Experiments show that MegaAvatar achieves high-quality talking avatar generation with controllable body and head motion, speech-synchronized facial expressions, and consistent identity preservation. MegaAvatar also supports inference with flexible resolutions and video lengths. Codes, dataset, models will be avaliable in https://github.com/Jeoyal/MegaAvatar

As state-of-the-art text-to-image flow models achieve near-photorealistic quality, controlling their outputs, e.g., suppressing harmful content while promoting benign alternatives, has become a central challenge. The current steering paradigm consists of adding a global steering vector to selected activations. While functional, a fixed and example-agnostic vector applied uniformly along the entire trajectory cannot adapt to the changing state of the generation and often causes unintended global changes. We introduce Steering Fields, a generalization of steering vectors that adaptively re-estimates the steering direction at each step of the generative process. Steering Fields operate on the noisy states of flow models, expose a continuous trade-off between steering strength and content preservation, and are compositional, enabling the simultaneous induction and inhibition of concepts, setting a new state of the art on safety steering benchmarks. Despite using no explicit spatial masks or object priors, the trajectory-adaptive estimation naturally preserves local structure, in a manner reminiscent of image editing. In fact, Steering Fields can serve as a structure-preserving image-editing technique that achieves state-of-the-art semantic fidelity (CLIP, VQAScore), while remaining model-agnostic and inversion-free.

Recent video generation is increasingly realistic and controllable, yet video editing remains less developed, particularly for precise local edits that must preserve the original scene dynamics. Video scene text editing replaces text on scene surfaces, such as storefront signs, whiteboards, and product labels, while preserving the surrounding content, motion, and camera dynamics. Although scene text editing is well studied for images, video scene text editing that achieves high visual quality, temporal consistency, and edit locality remains underexplored. Existing resources offer limited paired real-video data, and general video-editing metrics do not directly measure whether the requested text remains correct over time. We introduce ViTeX-Bench, a benchmark suite comprising ViTeX-Dataset and a three-axis evaluation protocol. The dataset contains 387 real-world 720p videos with text-region masks and editing instructions: 230 provide reviewed, pipeline-generated paired edits for training, and 157 form a frozen evaluation split. The protocol evaluates text correctness, visual and temporal quality, and edit locality through 13 metrics, with one primary metric per axis and a Pareto comparison of their trade-offs. OCR calibration, human evaluation, and annotation-sensitivity analyses support the interpretation of these scores. Across eight baselines from four editing families, accurate text, temporal stability, and scene preservation remain difficult to achieve together. We also release ViTeX-Edit-14B, an open-source reference editor fine-tuned on the paired training split with motion-aligned glyph-video conditioning. It achieves CharAcc 0.688, the highest mean among the evaluated video-native editors, and the lowest comparable text-crop Warp among raw editor outputs. ViTeX-Bench provides a reproducible foundation for studying these trade-offs in video scene text editing.

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.

Federated learning (FL) on memory-constrained edge devices faces a dilemma: first-order (FO) optimization (i.e., backpropagation) demands substantial memory, whereas zeroth-order (ZO) optimization suffers from severe convergence slowdown. To resolve this dilemma, we introduce HO-FL, a hybrid-order FL framework that trains a model's bottom segment with ZO optimization and its top segment with FO optimization. Each device can flexibly select its order boundary according to its memory budget while participating in the training of the same global model. Moreover, our convergence analysis reveals a new, fundamental trade-off: clients with larger FO-trained segments can provide more accurate updates, but favoring them can underrepresent other clients' data. We connect this trade-off to the bias and variance of actual multi-step local updates, yielding a sampling optimization problem and a practical dimension-aware approximation with direct model averaging. Experiments on language tasks examine task performance, client memory, and sampling under data heterogeneity. The results show that hybrid-order local training can retain much of the full-FO performance with substantially lower client memory requirements. Our code is available at https://github.com/HKU-WILL-Lab/HO-FL.

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.

Matching problems are ubiquitous in data science as they enable the alignment of structured objects and distributions. While existing solvers are often tailored to specific matching formulations, we unify a broad class of such problems within a common mathematical and optimization framework based on duality theory. Theoretically, we demonstrate that matching objectives decomposable as a difference of convex (DC) functions can be recast as implicit registration problems. This connection links matching to another well-studied class of objectives and yields a dual formulation amenable to natural optimization strategies. We then apply these findings to quadratic matching (QM) problems, which admit DC decompositions and for which we provide extensive convergence guarantees. Our framework applies to Gromov-Wasserstein (GW), as well as its unbalanced formulation and several variants, which are increasingly popular QM problems. Numerically, we implement our algorithms at scale for various data modalities such as graphs, point clouds, meshes, and word embeddings. Finally, our modular approach allows us to explore new formulations such as fracture matching, broadening the scope of problems that can be addressed within this framework..

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.

Safe and efficient quadruped navigation over unfamiliar terrain requires predicting terrain-robot interaction before contact: geometry and visual appearance alone cannot reveal how the robot will slip, load its feet, or expend energy. This paper presents a continual learning pipeline that uses locomotion experience to learn these interaction outcomes from pre-contact images and continually updates the predictions as new contacts are observed. Pre-contact descriptors, produced by a DINOv3 backbone model frozen during training, are mapped to five proprioceptive indicators weighted according to measurement reliability: planar foot slip, mean normal ground-reaction force, traction index, cost of transport, and touchdown loading rate. A compact evidential regressor allows us to predict these indicators together with aleatoric and epistemic uncertainty from the visual descriptors. Continual adaptation combines bounded experience replay with a validation gate: candidate models replace the deployed predictor only when they improve performance on recent held-out data while keeping degradation on historical held-out data within a prescribed tolerance. Predictions and epistemic uncertainty are projected into a local multilayer map and combined into a conservative traversability score map whose property weights can be adjusted without retraining. The resulting map is used for downstream navigation tests. The ROS2 implementation supports evaluation on a Unitree Go2 in simulation and on hardware, with models trained separately in each domain. On a sequential hardware stream over three previously unseen terrains, gated replay reduces final anchor negative log-likelihood (NLL) degradation by 23.1% relative to replay without the gate while attaining similar new-terrain adaptation.

Physical parameter estimation from video aims to recover the parameters of a known family of governing dynamical equations from pixel observations. Existing identifiability theory for this setting has focused on linear time-invariant (LTI) second-order systems, leaving open what can be identified for nonlinear scalar dynamics. We develop an identifiability theory for nonlinear scalar second-order ODEs, organized by how their velocity dependence interacts with changes of the learned state coordinate. Under a shared non-collapsed state map and explicit same-state velocity-coverage conditions, we show that parameter identifiability depends on the ODE family: some parameters are uniquely identifiable, while in other families only invariant parameter combinations are identifiable or external physical calibration is required. For laws that are at most linear in velocity, compatibility forces affine coordinate alignment, yielding explicit parameter relations, invariants, and calibration conditions. This affine conclusion extends to broader finite velocity-feature families when coordinate curvature can be separated from the declared velocity dependence. For families admitting a squared-velocity term, nonlinear coordinate ambiguity can remain; a law-derived normalization instead enables affine comparison between canonical laws. Experiments on synthetic systems and real pendulum and free-fall videos support the predicted parameter relations, coverage effects, and calibration requirements.

Self-consistency samples many reasoning trajectories and aggregates their final answers, treating the LLM as a black box that returns one answer per trajectory. Yet the final answer of each trajectory is sampled from a softmax vector that is available from the model's log-probabilities. We refer to this as the grey-box setting in which each trajectory reveals this answer distribution rather than a single draw from it. We formulate efficient inference in this setting as sequential mode identification with distribution-valued observations: sample trajectories one at a time and stop as soon as the LLM's modal answer is identified at a prescribed confidence level. We characterize the asymptotic stopping rate of mode identification with distribution-valued observations exactly and show that it is never worse than the black-box rate. We then propose the ASC-D algorithm, a betting stopping rule that attains this asymptotic stopping rate. On MMLU-Redux, ASC-D uses $46.4$--$95.6%$ fewer trajectories than answer-only adaptive self-consistency baselines and achieves the highest fixed-budget correct-certification rate across three open-source models.

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.

A deep classifier is defined not only by the decision it produces, but also by the sequence of transformations through which that decision is formed. Treating this evolution as a dynamical system across layers provides a natural framework for asking how decision geometry emerges through depth and how far back we can trace a boundary's dynamical signature. We model a feed-forward classifier as a finite, nonautonomous discrete dynamical system, with layers playing the role of discrete time steps. We study the Finite-Time Maximum Lyapunov Exponent (FTMLE) of the data samples' dynamical trajectory through depths of the classifier. The FTMLE measures the rate of convergence/divergence of nearby trajectories. We move the observation endpoint backward from probabilities to logits and then to hidden representations. For Gaussian classes, we prove that probability-level FTMLE carries a clear geometric signature of the decision boundary, with its dominant direction aligned with the boundary normal. Moving one step backward to the logits, we prove this relationship is no longer universal but depends critically on how the classifier is trained, particularly on the choice of loss function. Moving further backward to the hidden representation, the connection becomes more conditional: boundary-related FTMLE can persist, but only under identifiable structural conditions. We propose geometry-aware fine-tuning for restructuring the classifier's hidden FTMLE, and propose conditions for guaranteed concentration of high hidden FTMLE near the decision boundary. Through our numerical results, we show the generality and validity of our theoretical results. Understanding the evolution of data samples as traveling through the layers of classifier provides a principled foundation for identifying where boundary-relevant sensitivity emerges and for developing layer-aware regularization strategies.

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.

Asynchronous SGD is a popular algorithm for distributed learning where each client's gradient update is applied on arrival. This leads to a speed-up, but also an increased vulnerability to attacks, as fast clients can dominate the total update. We introduce Throttle, a Byzantine-robust generalization of asynchronous SGD where the key idea is to exponentially down-weight updates from faster clients by a factor $q$. Both asynchronous SGD ($q=1$) and synchronous Byzantine-robust SGD ($q\to\infty$) correspond to specific settings of Throttle. We provide a theoretical analysis of the convergence rate and validate the robustness to attacks both theoretically and empirically. Remarkably, our experiments show that this down-weighting mechanism can also improve performance over standard asynchronous SGD even in the non-Byzantine setting.

Casting Bayesian inference as a neural network optimization problem targeting an amortized posterior is attractive, as it extends to otherwise intractable statistical models and offers near instantaneous inference for new datasets after prepaying the training cost. Although theory guarantees faithfulness under ideal convergence, practical amortized inference still requires iterating over architectures and optimization choices and ultimately ``satisficing'' under finite simulation, compute, and time budgets. Even the best-performing solution may thus retain avoidable representation gaps that typically require problem-specific fixes. Here, we propose a generic alternative which improves training dynamics with auxiliary guidance losses applied to internal representations. Specifically, we show how such guidance leads to faster convergence when training data is abundant and to better performance when it is scarce. We formalize representation gaps as getting stuck in a local optimum at the information bottleneck between the parts of the network tasked with feature learning and those tasked with conditional distribution learning, and offer a generic diagnostic to separate summary failures from inference failures. Finally, we demonstrate that auxiliary supervision improves convergence speed and accuracy on a range of challenging real-world inference problems.

Pretrained tabular generators can reproduce training records even when aggregate utility remains high. When retraining is unavailable or too costly, sampling and release are the remaining intervention points. We present PEG-Tab (Post-Training Energy Guidance for Tabular Synthesis), a post-training repair and release-control framework for frozen tabular generators. For each generated row, a generator-native operator creates two alternatives. A shared calibrated score compares the three candidates, favours lower-risk records, and applies a final release check. We instantiate this interface for GReaT, CTGAN, TVAE, and TabDDPM without updating their parameters. Across five datasets and four generator families, PEG-Tab reduces mean Near Copy from $0.078$ to $0.027$ and lowers aggregate Exact Copy to zero. Relative to a $3\times$ post hoc filter, it retains higher utility in 12 of 16 transfer settings and Pareto-dominates the filter in eight. Gains are concentrated in copy and proximity-related risks.

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.

Partial Optimal Transport (POT) extends the classical optimal transport problem by relaxing the strict mass conservation constraint, enabling its use in a wide range of real-world applications. In many of these settings, sparse transport plans are preferred for their interpretability and computational benefits. While smooth and strongly convex regularizers - such as quadratic or elastic net - have been vastly used in various machine learning applications to induce sparsity and accelerate computation, they have received less algorithmic attention compared to entropic approaches for computational POT. In this paper, we propose a new optimization framework that leverages these regularizers through a penalty-based reformulation, enabling efficient gradient-based updates while preserving the structure of the original problem. Our method accommodates a broad class of regularizers that promote structured and sparse transport plans. Building on this formulation, we design an accelerated first-order algorithm that alternates between smooth updates and simple projection steps. Through empirical benchmarks on color transfer, domain adaptation, and point cloud registration, our approach consistently outperforms established baselines - achieving lower transport cost, higher sparsity, and faster convergence - making it a practical and scalable solution for modern transport problems.

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 consider simulation-based Bayesian inference (SBI) for the parameters of models with intractable likelihoods but tractable forward simulation. Building on Gaussian mixtures-of-experts surrogates, as a first contribution we develop a sequential procedure for posterior estimation in which progressively localized, data informed, conditional density approximations are used as proposal distributions. A final surrogate of the posterior distribution is then corrected using an importance sampling step that introduces a locally amortized likelihood-to-evidence ratio estimator. A second contribution is localized simulation-based calibration (SBC). Localized SBC probe calibration over neighborhoods that are deliberately broader than the available posterior, at low additional computational cost. Rather than repeatedly running the full inference procedure for each simulated pseudo-observation, localized SBC fits the local surrogate and ratio estimator only once for each local design, and reuses them across all pseudo-observations. This approach is particularly appealing for SBI applications. We evaluate both contributions on three case studies, including a real-data epidemiological application.

In many statistical settings, the available data and maintained assumptions do not suffice to uniquely identify the model parameters of interest. In such cases, one can only identify sets which are guaranteed to contain the true parameters. These are often characterized through linear programs that optimize over models compatible with the observed data. These programs can be infinite-dimensional in the optimizer and the number of constraints. We provide a unified way to characterize and solve such optimization problems by phrasing them as optimal transport problems on path spaces. This allows us to regularize the problem with an entropy penalty, recasting it as a multi-marginal entropic optimal transport problem, which can be solved efficiently via Sinkhorn iterations. In addition, it allows us to establish convergence of the regularized value to the sharpest bound, derive consistency rates for a plug-in estimator, and obtain asymptotic distribution for approximate bounds. The method is general and accommodates settings ranging from instrumental variable models with continuous variables to welfare estimation in heterogeneous demand models. We verify the statistical and computational properties in simulations and provide an application to demand estimation.

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.