Distribution Matching

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Distribution matching studies how to compare or align probability distributions, often when individual examples cannot be paired, to support generation, transfer, compression, and evaluation. Common tools include optimal transport and Wasserstein distances, kernel maximum mean discrepancy, divergences such as KL and total variation, and moment, quantile, or feature-space matching. These methods are used in generative modeling, dataset distillation, domain adaptation, representation learning, and distribution testing. A central tension is that results depend on the chosen representation and discrepancy: matching global or marginal statistics can miss modes, dependencies, or task-relevant structure, while richer comparisons can be costly or unstable.

Latest papers

80 papers13 papers in the last four weeks, up 225% on the four weeks before. 0.1% of all new papers.

When Does Training on Synthetic Data Provably Work?
Oct 20, 2026Leroy Odunlami, Tobias Riedlinger, Hanno GottschalkSynthetic-to-Real Domain Adaptation Covariate Shift
Institute of Mathematics, Technische Universität Berlin, Berlin, Germany
QuAD: Quantitative Assessment via Distribution-Alignment for Qualitative Data Quality Enabled by a Content-Aware Multi-Agent System
Oct 16, 2026Wenshuo Zhang, Leixian Shen, Qiqi Zhou +6Automated Evaluation Distribution Matching
The Hong Kong University of Science and Technology · Shanghai Jiao Tong University · The Hong Kong University of Science and Technology (Guangzhou)
Hypothesis Selection via Weighted Medians
Oct 14, 2026Liang-Yu ZouTV Distance Computation Statistical Learning Theory
Aarhus University
Constant-Curvature Sliced Gromov-Wasserstein for Heterogeneous Cross-Curvature Alignment
Oct 5, 2026Shanglin Li, Wenjing Lu, Muyang Li +2Distribution Matching Geometric Representation Learning
BIFOLD, Germany · Technical University of Berlin, Germany · RIKEN AIP, Japan +4
DriftTTS: Few-Step Text-to-Speech Without Distillation via Distribution-Matching Drift
Oct 2, 2026Mohammad Nur Hossain Khan, Subrata Biswas, Bashima IslamTTS Synthesis Distribution Matching
University of Massachusetts Amherst, MA, USA · Worcester Polytechnic Institute, MA, USA
Distribution Matching Evolutionary Algorithms for Rare Event Sampling
Oct 2, 2026Yonatan Gideoni, Yarin GalDistribution Matching Evolutionary Optimization
University of Oxford
Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributions
Oct 1, 2026Leyang Wang, Yakun Wang, Song Liu +1Distribution Shift Distribution Shift Detection
Department of Mathematical Informatics, The University of Tokyo, Japan · Center for Advanced Intelligence Project, RIKEN, Japan · School of Mathematics, University of Bristol, United Kingdom
How Divergence Becomes Decision Flips in Compressed Language Models
Sep 30, 2026Beatriz Almeida FelicioLLM Evaluation LLM Compression
Instituto de Informática (INF) Universidade Federal de Goiás (UFG)
Nonparametric Distribution Matching for Self-Supervised Whole-Slide Image Condensation
Sep 30, 2026Duong M. Nguyen, Trong Nghia Hoang, Hang Thi Nguyen +3Computational Pathology Distribution Matching
University of Illinois Urbana-Champaign · Washington State University · Hanoi Medical University +2
Reactive Real-Time Flow Policies via Asynchronous Distribution Alignment
Sep 29, 2026Moritz Zoellner, Reece O'Mahoney, Ioannis Havoutis +1Robot Policy Learning Efficient VLA Model Inference
Department of Computer Science, Purdue University · Oxford Robotics Institute, University of Oxford
Unifying Distributional Training for One-Step Visual Generation
Sep 28, 2026Chi Zhang, Shi Haoyang, Yueyi Liu +9Gaussian Mixture Models T2I Generation
Tsinghua University · Fudan University · Xi’an Jiaotong University +4
Sample What You Say: Aligning Language Models to Sample the Distributions They State
Sep 28, 2026Kasra Arabi, Virginia Smith, Chhavi YadavRL for Language Models Group Relative Policy Optimization
New York University · Carnegie Mellon University
PSM: Dataset Distillation Based on Precise Statistical Matching by Difficulty
Sep 28, 2026Hongxu Ma, Guang Li, Shijie Wang +6Distribution Matching Dataset Distillation
Zhejiang University · Hokkaido University · The University of Queensland +3
ViRDM: Taming Representation Distribution Matching for Few-Step Causal Video Generation
Sep 24, 2026Zichong Meng, Chongjian Ge, Chun-Hao P. Huang +2Diffusion Model Distillation Distribution Matching
Northeastern University · Adobe Research
Divergence Timing and Cumulative Disagreement under KV-Cache Eviction
Sep 15, 2026Xinyue Luo, Fei YuKV Caching KV-Cache Eviction
Wealth AI Lab, Ant Group
MaD-RL: Matching Distributions for Calibrating LLMs with Reinforcement Learning
Sep 12, 2026Sourabh Kulkarni, Ksheeraj Sai Vepuri, Basar Demir +8Distribution Matching RL for Language Models
Meta Superintelligence Labs
Accuracy is Not Enough: A Divergence-Based Approach to Evaluate Fidelity Loss in Quantized LLMs
Sep 7, 2026Shahzeb Qamar, Lorenz Sparrenberg, Christian Bauckhage +5LLM Quantization LLM Evaluation
Fraunhofer IAIS, Germany · PhenoRob Cluster of Excellence, University of Bonn, Germany · Lamarr Institute for Machine Learning and Artificial Intelligence, Germany +4
On the Indistinguishability of Human v/s AI Generated Text
Aug 27, 2026Jaee Ponde, Aritra Das, Mihir More +1Generative AI Evaluation Distribution Matching
Truth Audit Labs
Joint Distribution Alignment for Universal Domain Adaptation
Aug 25, 2026Shizhe Li, Hongshan Pu, Mengying Xie +2Domain Adaptation Distribution Matching
School of Software Engineering, South China University of Technology, Guangzhou 510006, China · School of Future Technology, South China University of Technology, Guangzhou 511442, China · College of Computer Science, Chongqing University, Chongqing 400044, China
Mismatch Matters: On-Policy Distillation Beyond Token Agreement
Aug 10, 2026Zichao Yu, Chengzhi Yu, Shengze Xu +4Distribution Matching Language Model Distillation
The University of Hong Kong · University of Science and Technology of China · The Chinese University of Hong Kong
One-Sided Quantile Coupling for Flow Matching
Aug 2, 2026Jin-Young Kim, So-Yoon Cho, Hyun-Gyoon KimFlow Matching Image Generation
Independent Researcher · Division of Finance & AI, Hankuk University of Foreign Studies · Dept. of Financial Engineering, Ajou University
QQWorld: Quantile-Quantile Matching for World Model Regularization
Jul 30, 2026Zhoushun Yu, Xiaoyu Hu, Xiangyu XuWorld Model Learning World Model-Based Planning
Xi’an Jiaotong University
Amortized Moment Matching for Visual Generation
Jul 29, 2026Wenze Liu, Xintao Wang, Pengfei Wan +1One-Step Generative Modeling Distribution Matching
MMLab, CUHK · Work done at Kuaishou Technology. · Kling Team, Kuaishou Technology
Unbiased Open World Regularization for Fair Self-Supervised Learning
Jul 24, 2026L{é}o Nicollier, Marc Pic, Pablo Mus{é} +2Self-Supervised Learning Distribution Matching
CB, ATT · Université Paris-Saclay, CNRS, ENS Paris-Saclay, Centre Borelli, France · ATT +4
Three-Body Scattering for Generative Modeling
Jul 20, 2026Peng Sun, Zhenglin Cheng, Deyuan Liu +3One-Step Generative Modeling Distribution Matching
Westlake University · Zhejiang University · University College London
Distributional Matching for Vector Quantization: A Unified Theoretical and Empirical Framework
Jul 17, 2026Xianghong Fang, Litao Guo, Hengchao Chen +8Distribution Matching Vector Quantization
University of Toronto · The Hong Kong University of Science and Technology · Lehigh University +2
DiMaS: Distribution Matching for Steering Vision-Language-Action Models
Jul 15, 2026Pegah Khayatan, Sara Meziane, Jayneel Parekh +1Language-Conditioned Robot Manipulation Distribution Matching
ISIR, Sorbonne Universit´e, Paris, France · Valeo.ai, Paris, France
Improving Medical Image Generative Models with Fréchet Distance Loss
Jul 14, 2026Andrew Marshall, Xuanang Xu, Xiaoran Zhang +3Synthetic Data Augmentation Distribution Matching
Department of Biomedical Engineering, Yale University · Department of Radiology & Biomedical Imaging, Yale University · Department of Electrical Engineering, Yale University
Normative Alignment of Recommender Systems via Internal Label Shift
Jul 12, 2026Johannes Kruse, Kasper Lindskow, Michael Riis Andersen +4Distribution Matching Recommender Systems
JP/Politikens Media Group · Technical University of Denmark · Copenhagen Business School +4
Beyond Random Sampling: Distribution-Aware Alignment for Semi-Supervised Medical Image Segmentation
Jul 5, 2026Weihao Yan, Yeqiang Qian, Yi Dong +1Data Augmentation Data Selection
School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China · Department of Ultrasound, Xinhua Hospital Affiliated to Shanghai Jiao Tong University School of Medicine, Shanghai, China

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When Does Training on Synthetic Data Provably Work?

Leroy Odunlami, Tobias Riedlinger, Hanno Gottschalk

Institute of Mathematics, Technische Universität Berlin, Berlin, Germany

Synthetic-to-Real Domain Adaptation Covariate Shift Distribution Matching Synthetic Data Generation

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High-quality training data are a major bottleneck in machine learning, motivating increasing use of artificially generated data. We study when a binary classifier trained on synthetic data transfers successfully to a real distribution, under a shared conditional label distribution. First, we derive finite-sample excess-error bounds when the real covariate distribution is absolutely continuous with respect to the synthetic distribution under a controlled density ratio. Second, we study the partially and fully singular case, where the real distribution has mass outside the synthetic one. If the hypothesis class is sufficiently expressive, synthetic risk alone cannot uniformly control real-world error: a classifier can be nearly optimal on synthetic data while approaching worst-case error on the uncovered real region, even when the distributions are arbitrarily close in Wasserstein distance. For function classes where hypotheses and the log-odds of the conditional label probability are Lipschitz, we recover a bound in terms of the probability that a real sample lies outside the reach of the synthetic data, restoring a transfer guarantee even in the fully singular case. Experiments confirm this in controlled low-dimensional settings and on 32,200 images generated as counterparts to real ImageNet images by four state-of-the-art generators: an adversarial classifier reaches 0.5% error on the synthetic domain but 99.25% error on the real domain, while ordinarily trained architectures show positively correlated synthetic and real test errors. Synthetic data should be budgeted at high sample counts and models validated on real data.