Distribution Matching

Recent advances in representation learning have highlighted the utility of constant-curvature models, such as hyperbolic and spherical spaces, for modeling complex data. Mixed-curvature models further enhance this by integrating multiple constant-curvature components. However, these models typically learn each component space independently because spaces with different curvatures are inherently heterogeneous and lack a unified metric. Consequently, they lack explicit mechanisms to enforce geometric consistency across various spaces. Moreover, the problem of comparing probability distributions across mixed-curvature spaces remains unexplored. To compare distributions on heterogeneous spaces, Gromov-Wasserstein (GW) distances provide a principled framework by aligning their intra-space geometries. Building on this, we propose constant-curvature sliced Gromov-Wasserstein (CCSGW), a novel divergence for aligning distributions supported on heterogeneous constant-curvature spaces. We first introduce the missing geodesic-based one-dimensional projections for spherical spaces, and then extend sliced GW to constant-curvature spaces, enabling efficient and principled comparison across manifolds with different curvatures. This formulation preserves intrinsic geometric relationships while avoiding the high computational cost. We provide theoretical analysis showing that CCSGW controls intrinsic geometric discrepancy across heterogeneous spaces, promoting distribution-level geometric consistency. By integrating CCSGW into existing mixed-curvature learning tasks, including graph anomaly detection, graph node classification, and multimodal learning, we observe consistent performance gains across diverse settings.

Comparing two high-dimensional discrete distributions has always been a challenging task due to the exponentially growing state space and complex changes in interactions. A recent work suggests comparing distributions through a vector field trained using flow matching between two continuous distributions. The resulting vector field at mid-point vanishes if and only if two distributions identical. However, such a flow-based criterion does not naturally apply to discrete distributions. We extend this principle to the discrete domain and introduce the \emph{Zero Flux} criterion, a discrepancy based on local probability fluxes. Under independent coupling, we show that all local probability fluxes vanish at the midpoint if and only if two distributions are the same. This discrepancy decomposes the joint distributional difference into smaller, local contributions and can be efficiently estimated from samples. We establish finite sample error bounds for our estimator. Experiments on synthetic and real categorical data demonstrate reliable recovery of sparse dependence signals and stable tracking of distribution shifts in high dimensions.

Compression reports summarize how far a compressed language model moved from the dense one, usually by a KL divergence; a deployment that relies on the dense model's outputs needs to know how many of its decisions changed. We show that total variation, not KL, answers this directly. Across 802 compressed and perturbed copies of 19 open models on five corpora and nine mechanically unrelated perturbation families, the rate at which the arg-max token changes (the \emph{flip rate}) tracks total variation at a ratio with median $1.05$, with no fitted constant. KL converts into flips only through its square root and a factor that varies fourfold across models and corpora, because KL averages over tokens before the root is taken; first-order statistics averaged per token, such as Hellinger distance, avoid this, but reports rarely give them. As a result, of two compressors reported on different models and corpora whose flip rates differ by at least $10$, KL assigns the smaller divergence to the one that changes more decisions in $11$ of cases, total variation in $1$. Two pre-registered tests mark the limits: on a held-out code corpus the ratio held for all eight models while three predictions about KL each failed for half of them or more, and on three new models with real kernels it stayed in its band for 37 of 38 checkpoints but fell below one on code for two models. In vLLM speculative decoding, total variation measured under teacher forcing predicts greedy draft acceptance with a mean relative error of $1.1$--$2.4$, without the task-specific calibration that KL needs.

Histological whole-slide images (WSIs) are central to computational pathology but pose severe computational challenges due to their extremely high resolution, often spanning several gigabytes per slide. To enable scalable learning, existing methods apply self-supervised data condensation to reduce computational cost, but typically rely on heuristic prototype learning and do not explicitly preserve learning-relevant feature distributions for downstream tasks. In response, we introduce a principled reformulation of WSI condensation as a distribution-matching problem under a fixed representational lens, and develop NICER, a tractable approximation framework based on a nonparametric prior with slide-adaptive capacity. Experiments on five histopathology datasets, together with clinical evaluation from a board-certified pathologist, show that NICER consistently outperforms prior methods, achieving an average accuracy improvement of 7.44% while offering improved efficiency-accuracy trade-offs, highlighting the benefits of principled, distribution-aware condensation for scalable histological representation learning. Source codes are available in https://github.com/nmduonggg/NICER.

Generalist robot policies such as vision-language-action models (VLAs) have achieved remarkable generalization, but their inference delays can conflict with the demands of real-time control. Asynchronous execution avoids pauses between action chunks by predicting the next sequence of actions while the robot carries out the previous one. In this paper, we study whether asynchronous execution produces the same action distribution as the original VLA. We find that, for non-Markovian demonstrations, asynchronous execution can produce a fundamentally different action distribution, which can limit the policy's reactivity. In our method, we seek to restore this reactivity by aligning the asynchronously produced action distribution with that of the original VLA through two complementary mechanisms. First, Recursive Flow-Field Distillation trains the asynchronous policy using the VLA's action-generation flow. We characterize the learned distribution theoretically and show experimentally that our asynchronous policy can generate nearly the full range of actions the original VLA would produce, while existing asynchronous methods recover only a fraction of that range. Second, Propose-Resolve prepares multiple action sequences asynchronously and uses the latest observation to select among them based on a lightweight approximation of their likelihood under the VLA's action distribution. Our resulting method matches the original VLA's success on LIBERO and retains about 80% of its success on RoboMimic, about 30 percentage points more than existing asynchronous methods.

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

Language models are increasingly used to sample from a specified distribution, for instance, to simulate survey respondents or generate synthetic data. Instruction-tuned models can state such a distribution correctly and still fail to sample from it. Prompting and changes to decoding reduce this mismatch only partly, which motivates training with policy optimization. Group relative policy optimization (GRPO) is a natural fit for this problem because it already samples a group of rollouts per prompt, and the group's empirical distribution can be compared with the target. However, scoring the group as a whole gives every rollout the same reward. Group-relative centering then sets all advantages to zero, and the model receives no learning signal. To give each rollout its own signal, we introduce the witness advantage, a per-rollout advantage derived from maximum mean discrepancy (MMD). It trains a model to match a target distribution over a finite set of outcomes. The MMD between the model's distribution and the target has a witness function that measures how over- or under-produced each outcome is. Each rollout's advantage estimates the negative witness at its outcome, so a rollout is rewarded for an outcome the group under-produces and penalized for one it over-produces. The witness advantage is computed in closed form from the group's outcome counts, and we use it as the reward in GRPO. On unseen target distributions, training with the witness advantage substantially reduces the total variation distance to the target while largely preserving the model's general capabilities.

Dataset distillation (DD) condenses a large original dataset into a small distilled dataset with high training utility. Decoupled statistical matching methods substantially reduce distillation time and memory overhead while achieving strong performance. However, they typically supervise all distilled samples using running statistics estimated from the entire original dataset. These statistics mainly capture the average feature distribution while overlooking differences in sample difficulty, limiting their ability to characterize the difficulty structure of the original data. To address this issue, we propose Precise Statistical Matching (PSM) by difficulty. After pretraining, PSM uses the Global Precision Score (GPS) to estimate image difficulty, ranks the samples within each class, and partitions each class into IPC (images per class) difficulty groups. During distillation, Statistics Updated Again (SUA) updates the teacher's batch normalization (BN) running statistics through forward passes on original samples from each group, providing difficulty-specific supervision for the corresponding distilled batch. Meanwhile, Initial Sample Screening (ISS) initializes distilled samples using original images from the corresponding difficulty group, providing an effective starting point for precise matching. Experiments across multiple datasets and model architectures demonstrate that PSM broadens the difficulty range of distilled samples and improves downstream performance in most evaluated settings. Code will be released.

Few-step autoregressive (AR) video diffusion enables low-latency streaming generation, but existing post-training methods predominantly rely on Distribution Matching Distillation (DMD), requiring both a large pretrained teacher and an online critic to estimate distributional discrepancies through diffusion scores. In this work, we ask whether this resource-intensive teacher--critic stack can be eliminated by post-training only the generator against a precomputed target distribution. Drawing inspiration from representation distribution matching (RDM) for one-step image generation, we systematically study its transfer to few-step causal video generation and identify three key barriers: a memory-intractable gradient path, a distinct video optimization regime, and representation distributions that underconstrain temporal dynamics. We introduce ViRDM, a teacher- and critic-free video post-training recipe that addresses these barriers sequentially. By coupling RDM with stochastically truncated clean-exit supervision, a lightweight VAE decoder, and staged vector--Jacobian products, ViRDM makes representation distribution matching memory-feasible for multi-step causal video rollouts. We further establish effective generated-population and initialization regimes for video RDM, and introduce lightweight dynamics regularization to compensate for the underconstrained temporal dynamics. ViRDM turns three-network distillation into generator-only post-training, reducing GPU memory use and training time while improving video quality. With only 20 generator updates, the recipe reaches 84.87 on the official VBench evaluation, outperforming the previous best few-step causal baseline by 0.36, while requiring 16 A100 GPU-hours. We additionally report exploratory results demonstrating the potential of the same recipe for lower causal sampling budget and for one-, two-, and four-step bidirectional generation.

KV-cache eviction perturbs the conditional token distributions governing autoregressive generation. We investigate how first-divergence timing and subsequent token mismatch determine cumulative disagreement. We derive an exact decomposition under a specified stepwise maximal coupling: the expected mismatch fraction equals a first-mismatch contribution plus post-divergence exposure multiplied by its mismatch rate. An explicit construction over unrestricted autoregressive kernel pairs realizes the sharp interval of risks compatible with a finite divergence-aligned observation window. Residual-branch conditional Monte Carlo provides unbiased joint estimates of occurrence, occupation, and window/tail contributions, with per-replicate variance dominance for total token loss. Complete trajectories from Meta-Llama-3.1-8B-Instruct and Qwen2.5-7B-Instruct show that SnapKV at 50% retention enters divergence later and less often than SnapKV-512 or recent-token retention with the same 50% prompt-cache budget, while post-divergence total variation (TV) remains high. In an exploratory analysis of 288 documents, post-divergence exposure accounts for 85-90% of four aggregate mismatch gaps. On 288 independent documents at 90% retention, prespecified comparisons show higher branch-aligned TV in the late than in the early window in both models.

On-policy distillation (OPD) has emerged as a core component of modern LLM post-training pipelines, yet we reveal a failure mode: degenerate agreement, where students exploit repetitive loops to achieve near-perfect token agreement with the teacher despite globally flawed responses. We therefore shift our focus from agreement to teacher-student mismatch, and find that mismatch tokens can be mainly categorized into two types: student-excess tokens and student-deficit tokens. Student-excess tokens are generated by the student but assigned near-zero probability by the teacher; their log-ratio corrections grow unbounded and destabilize the update. Student-deficit tokens, in contrast, are preferred by the teacher but rarely sampled by the student; their absence blocks the transfer of the teacher's reasoning patterns. To tackle these mismatch directions, we propose TIDE (Token-level Independent Deficit-Excess correction), which applies bounded Hellinger shaping to suppress the most severe sampled excesses and an analytic teacher top-$K$ injection to restore deficient probability mass without requiring deficit tokens to be sampled. Across mathematical reasoning benchmarks with multiple Qwen3 teacher-student pairs, TIDE consistently outperforms standard OPD and recent token-selection and reward-shaping baselines. Moreover, the gains of TIDE are more pronounced under strong teacher-student mismatch, where it improves Avg@8 from 6.9% to 20.3%, reduces average response length by a factor of 3.6, and substantially reduces formatting failures. Code is available at https://github.com/yzc-666/TIDE

Flow Matching trains continuous-time generative models by regressing the velocity field of a probability path between a simple source distribution and a target data distribution. The coupling that pairs source and target samples strongly affects optimization and sample quality, but structured couplings typically rely on mini-batch transport or assignment procedures whose cost grows at least quadratically in batch size. We propose Quantile Coupling Flow Matching (QC-FM), a lightweight one-sided coupling: rather than matching two pre-sampled batches, it samples only the data batch and constructs each paired source directly. Data ranks projected along a small number of random orthogonal directions are mapped to Gaussian quantiles, and the latent code is completed in the orthogonal complement by conditional Gaussian sampling. The construction is one-dimensional per slice, so the coupling requires no pairwise cost matrix and no assignment to solve. We show that, for each drawn frame, this coupling eliminates the irreducible regression variance along every selected slice and makes the ideal flow exactly straight there, while leaving the sampling prior unchanged: generation still starts from the standard Gaussian, and the training source deviates from it only through the copula of the slice codes, whose transport cost we bound. For training, we apply QC to an anchor subset and complete the remaining source slots with exact Gaussian samples, retaining the QC bias while preserving an explicit signal from the Baseline coupling. Across CIFAR-10, CelebA, FFHQ, and ImageNet-64, QC-FM improves over the Baseline under matched training budgets, reducing FID by up to 12.9%, and outperforms OT-CFM on all four datasets. These results suggest that preserving projected rank structure is a simple and scalable way to inject useful geometric bias into FM couplings without solving a mini-batch transport problem.

Latent world models enable efficient planning by predicting future states in a compact representation space, but their performance depends critically on the quality of the learned latent distribution. LeWorldModel (LeWM) regularizes its latents toward an isotropic Gaussian using the Epps-Pulley (EP) objective. We show that the corrective gradients of EP rapidly vanish for isolated tail samples, leaving heavy-tailed deviations insufficiently controlled. To address this limitation, we propose QQWorld, which replaces EP with a quantile-quantile matching objective that directly aligns projected latent samples with rank-matched Gaussian quantiles, thereby maintaining effective corrective gradients in the tails. We further develop cross-batch QQ, which enlarges the effective ranking pool using detached samples from previous batches, and characterize its bias-variance trade-off. Across four control environments, QQWorld effectively improves the average planning success rate of LeWM, while consistently yielding better Gaussian alignment and thinner latent tails.

We propose amortized moment matching, utilizing neural networks to learn data moments as distributional training signals. By casting diffusion denoisers through polynomial projections, we establish a general framework for moment amortization, revealing that an $n$-th degree projection explicitly identifies data moments up to order $n+1$. Derived from the tractable affine case, we instantiate the Amortized Fréchet Distance (AMFD) loss. Unlike FD-loss which relies on explicit marginal moment calculations, AMFD is able to dynamically learn conditional moments via an alternating, matrix-free optimization pipeline that effortlessly scales to high-dimensional data. When operating on global representation features, AMFD serves as a powerful post-training objective; empirically, its neural formulation yields more robust training dynamics than exact statistical matching, substantially surpassing the FD baseline on the FDr$^6$ metric and achieving superior one-step generation on ImageNet. Furthermore, it unlocks direct exploration within native generative spaces, suggesting that the first two moments can identify target distributions only in spaces with strong semantics. Finally, when scaled to text-to-image generation, the condition-aware nature of AMFD unlocks massive gains in instruction-following capabilities, enabling our one-step models to outperform their multi-step FLUX.2 [klein] 4B teachers on the GenEval benchmark while achieving on-par performance on PickScore. Code and checkpoints are available at https://github.com/poppuppy/amfd.

Despite recent advances, self-supervised learning (SSL) models and Joint-Embedding Predictive Architectures (JEPAs) remain susceptible to learning spurious biases in the dataset. These techniques rely on regularization, which prevents representation collapse by enforcing a global target distribution such as a multivariate Gaussian or a uniform distribution on the sphere. However, these global constraints are insufficient to prevent bias entanglement, as task-irrelevant features can still segregate the latent space into distinct sub-regions. While recent approaches like Entangling and Disentangling (EnD) and Fair Supervised Contrastive Learning (FSCL) empirically debias the latent space, we show that they act as partial approximations of conditional distribution matching. To enforce this matching explicitly, we propose Unbiased Open World Regularization (UOWReg), an encoder-only framework. We show that this shift from a global to a conditional objective guarantees statistical independence between the learned representations and the targeted attributes, regardless of the chosen target distribution. We empirically validate this framework across both Gaussian and spherical latent spaces, using statistical measures to enforce these target distributions. While conditional matching successfully mitigates bias with both distributions, we demonstrate that enforcing conditional uniformity on the sphere yields a lower linearprobing classification error. Empirically, UOWReg reduces Equalized Odds violations on the CelebA benchmark while maintaining competitive classification accuracy compared to existing encoder-only baselines. Furthermore, we introduce the Synthetic Engraving Task-a novel setting in which a dominant macro-structure masks a fine-grained micro-signature. We show that UOWReg effectively prevents the subpopulation collapse observed in standard SSL, successfully isolating micro-signatures even when heavily entangled with the global structure.

Modern generative models typically rely on an adversarial critic, a prescribed noise-to-data path, or an autoregressive factorization. Instead, we show that a proper distributional energy can induce sample-level motion and provide direct regression supervision for a one-step generator. Three-Body Scattering Modeling (TBSM) for generation turns the energy distance into a constant-size per-projectile interaction: each projectile is attracted toward one real source and repelled from one independently generated source. Conditioned on the projectile and its condition, its expectation equals the $2$-Wasserstein gradient-flow velocity of $\frac12D_E^2(P_θ,Q)$. A batch of $B$ frozen-target events yields $O(B)$ sample-level losses, each using one reference for its condition instead of the minibatch-wide all-pairs field used by methods such as Drifting Models. Tracking this conditional expectation online can reduce field noise. Using scattering in frozen image features, TBSM trains one-step generators on ImageNet-256, achieving FID${}=2.23$ with pixel-space PixelDiT-XL and FID${}=1.63$ with latent-space DiT-XL at NFE${}=1$. We provide a design map relating diffusion-related supervision, Drift-like dynamics, and GAN-like objectives. These results establish tracked scattering as a route to high-dimensional one-step generation. Code: https://github.com/sp12138/TBSM.

The effectiveness of modern visual representation learning and autoregressive models critically depends on vector quantization (VQ), which discretizes continuous feature representations using a learnable codebook. Despite its widespread use, existing VQ methods often suffer from training instability and codebook collapse, arising from gradient mismatch induced by the straight-through estimator and the under-utilization of code vectors. In this work, we show that both issues can be traced to a fundamental mismatch between the distributions of feature vectors and code vectors, leading to inefficient representation and information loss. Building on this observation, we propose a distributional matching framework for vector quantization. We introduce principled criteria for desirable VQ behavior and demonstrate through theoretical analysis and empirical evaluation that aligning feature and code vector distributions provides a unifying mechanism for mitigating training instability and codebook collapse. We instantiate this framework using a Wasserstein-based objective with an efficient closed-form under a mild Gaussian approximation, and further show that a nonparametric alternative based on maximum mean discrepancy yields comparable performance. Extensive experiments on visual tokenization benchmarks support the effectiveness and robustness of the proposed approach.

Flow-matching-based vision-language-action (VLA) models have emerged as powerful policies for robotic manipulation, yet a critical capability remains underexplored: fine-grained behavioral control, the ability to govern how a robot performs a task by intervening on its internal representations. Representation steering is a well-established interpretability tool for language and vision-language models, where behavioral features are typically encoded as linear directions, but we show that these classic methods fall short in VLAs. We propose DiMaS, a Distribution-Matching Steering strategy tailored to flow-matching VLAs, which transports between representation distributions rather than shifting along a fixed direction, and show that it effectively controls behavior across two state-of-the-art VLAs. We further examine the generalizability of this strategy as the tasks it is learned from and evaluated on grow increasingly dissimilar, characterizing where behavioral control transfers and where it weakens. Finally, through an analysis of the representation structure of the action expert, we explain why classical linear steering falls short in the visuomotor setting: behavioral features are linearly decodable but not linearly steerable, which motivates the distribution-matching design of DiMaS. Our code is publicly available at https://github.com/pegah-kh/dimas, with additional results and videos at https://pegah-kh.github.io/dimas/

Diffusion generative models have demonstrated immense potential for synthetic medical image generation. However, these models often struggle to capture complex morphological characteristics of heterogeneous tumors with irregular boundaries, limiting their utility for downstream clinical tasks such as segmentation. This limitation stems from the standard denoising objective: minimizing a per-pixel error, which smooths high-variance irregular structures characteristic of tumors. To address this, we propose finetuning these generative models with Fréchet Distance loss (FD-loss). FD-loss aligns the first and second order feature statistics of real and generated images in a pretrained encoder space, encouraging the generator to capture complex structural variations characteristic of heterogeneous tumors. We integrate FD-loss across diverse architectural settings, using both natural- and medical-image encoders on multiple liver and brain cancer datasets spanning CT and MRI modalities. Downstream segmentation networks trained on our FD-regularized synthetic data consistently achieve superior performance, improving tumor DSC by >$$5\% over unregularized synthetic augmentation alone. Qualitative analysis suggests these gains are associated with more faithful tumor synthesis and fewer segmentation hallucinations. Our results show FD-loss as an effective regularizer for medical image generative models to improve clinical workflows.

We introduce NAILS (Normative Alignment of Recommender Systems via Internal Label Shift), a simple and scalable method for aligning recommendation outputs with target distributions over item-level attributes, such as categories. Recommender systems optimized solely for user engagement often fail to satisfy broader normative objectives, including fairness, diversity, and editorial values. NAILS modifies the user-conditional item distribution to induce a specified marginal distribution over attributes while preserving the preferences learned by an existing recommender system and requiring no model retraining. We formulate this problem as a form of label shift applied internally within a hierarchical classification framework. By adopting a stakeholder-centric perspective, NAILS enables recommendation outputs to be aligned with global normative objectives. Empirically, we show that NAILS consistently improves attribute-level alignment with minimal impact on user engagement, providing a practical mechanism for value-driven recommendation.

Precise medical image segmentation is crucial for clinical diagnosis and treatment planning, yet relies heavily on expensive expert annotations. Semi-supervised medical image segmentation (SSMIS) offers a cost-effective solution but typically operates under the assumption of independent and identically distributed (i.i.d.) data, defaulting to random sampling. While statistically valid at scale, this strategy suffers from severe representation bias in low-data regimes, failing to capture the heterogeneous medical data manifold. To address this, we propose a highly data-efficient framework driven by distribution alignment. First, we introduce an offline Distribution-Aware Sample Selection strategy. By leveraging Vision Foundation Models (VFMs) and our designed Density-K-Center algorithm, we explicitly identify representative structural anchors, establishing a more representative labeled domain. Second, to bridge the remaining distribution gap, we propose the Memory-guided Copy-Paste (MCP) module. Tailored for the inherent class imbalance in medical scans, MCP leverages a semantic memory mechanism to retrieve historically consistent priors for cross-domain alignment, encouraging semantic consistency. Coupled with an easy-to-hard progressive schedule, this framework effectively mitigates early-stage pseudo-label noise. Extensive experiments on six diverse 2D and 3D datasets demonstrate strong segmentation performance, particularly in extremely low-labeled scenarios (\eg, 1/16 ratio).

We elucidate the design space of Representation Distribution Matching (RDM), our name for the paradigm that trains a one-step image generator by matching generated and reference feature distributions under frozen pretrained encoders. We identify two design axes, how the distributions are compared and the representations they are compared in, and controlled studies along them yield three findings. First, the classical MMD, which could not train convincing generators a decade ago, becomes a strong and scalable objective once estimated right. Second, the generated batch is then the operative variable, with an optimum above 2048, far beyond customary batch sizes. Third, any single representation can be gamed, driven below the real score while images stay visibly fake, so we match against a balanced battery of encoders and evaluate with SW_r14, a Sliced-Wasserstein distance over 14 encoders that is independent of the training loss and resists gaming. Combining the preferred choices yields improved RDM (iRDM): it sets the one-step state of the art on ImageNet at SW_r14 1.30, corroborated by PickScore, a human-preference proxy our objective never optimizes, which prefers it over the prior best one-step generator on 71.2% of matched samples. The same recipe post-trains the four-step FLUX.2 [klein] into a one-step generator, surpassing the four-step version on GenEval, 0.826 to 0.794, and on PickScore, 22.76 to 22.58, in 90 H200 GPU-hours. Project page: https://alan-lanfeng.github.io/rdm/.

Recent advancements in scaling dataset distillation rely heavily on decoupled information extraction pipelines, comprising SQUEEZE, RECOVER, and RELABEL stages. Despite their scalability to large-scale datasets, these methods suffer from prohibitive computational overhead and poor cross-architecture generalization. In this paper, we reveal the root cause of these bottlenecks: the implicit dual-compression process, from data to model and back to images, inherently induces severe information loss. Crucially, we empirically and theoretically demonstrate that this loss creates a distribution shift that fundamentally compromises the widely adopted RELABEL strategy, transforming the pre-trained model into an unreliable labeler that yields sub-optimal labels. To overcome these critical flaws, we propose CIM, a novel, metric-driven framework that abandons the flawed dual-compression paradigm. Instead, CIM explicitly quantifies and minimizes the information gap between the original and synthetic datasets. By directly aligning the data distributions, our approach ensures high-fidelity information condensation and inherently satisfies the prerequisites for effective relabeling. Extensive experiments demonstrate that CIM establishes a new state-of-the-art. Notably, it distills ImageNet-1K at an IPC=10 in merely 80 minutes on a single RTX-4090 GPU, achieving an unprecedented 48.7% Top-1 accuracy on ResNet-18 and significantly outperforming previous SOTA approaches, such as NRR-DD and DELT, by 2.6% and 2.9%, respectively. Our code is available at https://github.com/LINs-lab/CIM.

The growing availability of trajectory datasets has fueled major advances in data-driven motion prediction. Yet, models trained on one dataset often fail to generalize beyond their training domain as a result of differences in scene layouts, agent behaviors, and sensing conditions. A framework that learns latent representations of datasets and quantifies their similarity using distributional metrics is presented. This large-scale study covers 24 major datasets, including the most widely used motion-prediction benchmarks, and shows that the resulting transferability scores strongly correlate with cross-dataset model performance. The results provide practical guidance for dataset selection, pretraining, and large-scale foundation models for motion prediction, paving the way toward more generalizable and robust predictive systems.

Diffusion and continuous-flow generative models achieve high-quality generation, and their deterministic sampling can be formulated as solving learned ODE dynamics. However, accurate ODE discretization often requires many steps, making efficient few-step generation a key challenge. Among acceleration strategies, reflow-based distillation simplifies teacher ODE trajectories so that a student model can approximate the teacher transport with fewer steps. We identify a theoretical limitation of this paradigm, namely that trajectory matching can under-determine the distribution induced by the student model. In particular, two student models can attain the same trajectory-matching loss while inducing different endpoint marginal distributions, which may lead to different generation quality. To address this limitation, we introduce a marginal-alignment regularizer that penalizes the discrepancy between the student-induced marginal and the corresponding teacher marginal at the endpoint of each distillation interval. The regularizer is computed by tracking log-density changes along the ODE induced by the student model and evaluating scores from the frozen teacher model, without requiring auxiliary trainable networks or adversarial optimization. The resulting framework applies uniformly to the reflow family, including vanilla reflow and piecewise reflow. We further prove a telescoping total-variation bound showing that local marginal alignment controls the final-time discrepancy between the student-induced and teacher-induced distributions. Experiments on benchmark backbones demonstrate the effectiveness of the proposed method for few-step generation.

Entity Matching (EM) is a core operation in the data integration pipeline, where records from different sources are compared to determine whether they refer to the same real-world entity. Recent work has incorporated domain information and low-resource learning techniques to better adapt EM systems to realistic settings. While these approaches have demonstrated strong performance, it remains unclear how they behave under varying data constraints and levels of supervision in practice. In this paper, we investigate a state-of-the-art method for low-resource, domain-aware EM--BEACON--and study how its performance is affected by different algorithmic choices and data availability conditions. We conduct a series of targeted experiments to evaluate these variations, providing deeper insight into the role of distribution alignment and the behavior of the BEACON framework.

In many modern applications of reinforcement learning (RL), the natural reward for a task of interest is inherently sparse: a reward of 0 is given everywhere except when the task is completed, when a reward of +1 is given. Training a policy to maximize such a sparse reward requires solving a challenging credit assignment problem, leading to slow or ineffective RL improvement. We propose a simple approach to transform a sparse outcome reward into a dense process reward. Our approach relies on training a discriminator to distinguish between previous successful and unsuccessful episodes, and using this discriminator to incentivize the RL-learned policy to match the state-action visitations of successful episodes, while avoiding those of unsuccessful episodes. By incentivizing the policy to match the visitations over all states, not just those that correspond to task success, this reward provides dense feedback on whether progress is being made towards task completion, and, we show, provably achieves this without changing the optimal policy. Focusing on finetuning of robotic control policies, we demonstrate that our approach leads to significantly faster RL finetuning performance on both simulated and real-world manipulation tasks, as compared to simply maximizing the sparse outcome reward.

Distribution shift between training and deployment is a pervasive challenge for modern AI systems. In many cases, the target marginals of covariates and response are known or specified through population-level observations, boundary conditions, properties of simulator configurations, or alignment-time distributional constraints. Such knowledge may provide valuable side information for regression estimation. We study this problem in the multivariate linear regression setting with a stable conditional mean $E[Y\mid X]$ across source and target, and identify the hybrid-loss estimator, which jointly incorporates both target marginals, as a benchmark target-aware estimator. Its direct computation, however, requires solving a coupled nonlinear optimization that is expensive at scale. Our main contribution is to develop and evaluate two computationally tractable alternatives: a constrained moment-matching estimator and a two-stage estimator that augments ordinary least squares with a calibration step. For all three estimators, we derive and compare closed-form asymptotic mean squared errors, yielding conditions under which the tractable alternatives match or closely approximate the hybrid benchmark, and regimes in which they do not. Monte Carlo experiments across three controlled shift regimes validate the theoretical results, investigate the accuracy-runtime tradeoffs among the three estimators, and translate into guidance on estimator choice. In particular, the two-stage estimator nearly matches the hybrid benchmark in the high signal-to-noise regime at essentially no additional cost, providing theoretical grounding for empirical observations in nonlinear settings.

Statistical matching combines partially overlapping datasets that share covariates $X$ but observe the target $Y$ and auxiliary variables $Z$ separately. Classical approaches typically invoke the conditional independence assumption (CIA), which makes the problem identifiable but fundamentally implies that the imported auxiliary variable provides no additional predictive power for $Y$ once $X$ is known. To capture this latent $Y$--$Z$ dependence, we propose a novel dependency-aware Schrödinger bridge for predictive statistical matching. Our approach couples the two separated databases by tilting the conservative CIA baseline with a transportation-based compatibility cost, recovering an informative joint distribution. The resulting statistical learning framework yields full probabilistic posterior rules for bidirectional imputation. Theoretically, we establish a sufficient condition under which the learned bridge strictly improves over the CIA baseline, alongside an exact joint recovery guarantee in the Gaussian setting under an appropriate cost. Across synthetic benchmarks and real-world datasets (CelebA and Adult), we demonstrate that our dependency-aware completion consistently improves downstream predictive utility, proving especially beneficial in settings like data recoding where the underlying population exhibits strong $Y$--$Z$ dependence.

Synthetic images are increasingly used to augment scarce real data for object detection. However, not all synthetic sets help equally, and the only way to know a set's value is to train a detector on it, which is slow and demands dense annotation. We ask whether a training-free metric can instead rank candidate synthetic training sets by their downstream utility. Existing image-set metrics such as FID, KID, and MMD compare two feature distributions with a single global statistic, which we show is mis-specified for detection-data selection in two ways: it is blind to per-image composition (object count, box scale, class mix), and even at fixed composition its global averaging washes out the appearance differences that separate high-mAP pools from low-mAP ones. We propose Conditional-Composition Domain Match (CCDM), which converts any feature-space distance into a composition-stratified comparison, matching candidate and target within metadata-defined strata without training a detector. On COCO and VisDrone-DET, the best CCDM variant ranks 19 candidate training sets in strong agreement with YOLOv8 mAP (Spearman \r{ho} = 0.97 and 0.96), outperforming FID, KID, and MMD. Furthermore, CCDM holds when reference metadata comes from detector pseudo-labels rather than ground-truth boxes.