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We provide a theoretical analysis for end-to-end training Discrete Flow Matching (DFM) generative models. DFM is a promising discrete generative modeling framework that learns the underlying generative dynamics by training a neural network…

Machine Learning · Computer Science 2025-09-29 Maojiang Su , Mingcheng Lu , Jerry Yao-Chieh Hu , Shang Wu , Zhao Song , Alex Reneau , Han Liu

The design space of discrete-space diffusion or flow generative models are significantly less well-understood than their continuous-space counterparts, with many works focusing only on a simple masked construction. In this work, we aim to…

We introduce Categorical Flow Maps, a flow-matching method for accelerated few-step generation of categorical data via self-distillation. Building on recent variational formulations of flow matching and the broader trend towards accelerated…

Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…

Machine Learning · Computer Science 2025-12-16 Yansong Gao , Yu Sun

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a…

Machine Learning · Computer Science 2026-05-11 Amin Karimi Monsefi , Dominic Culver , Nikhil Bhendawade , Manuel R. Ciosici , Yizhe Zhang , Irina Belousova

Understanding galaxy morphology evolution across cosmic time requires models that can generate realistic galaxy populations conditioned on redshift. In this work, we study efficient redshift-conditioned generative modeling for astrophysical…

Instrumentation and Methods for Astrophysics · Physics 2026-05-19 Tianyue Yang , Sandro Tacchella , Xiao Xue

While continuous diffusion models excel in modeling continuous distributions, their application to categorical data has been less effective. Recent work has shown that ratio-matching through score-entropy within a continuous-time discrete…

Machine Learning · Statistics 2026-02-09 Etrit Haxholli , Yeti Z. Gurbuz , Ogul Can , Eli Waxman

The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…

Computational Physics · Physics 2008-02-03 Hans E. Plesser , Dietmar Wendt

Single-image point cloud reconstruction must infer complete 3D geometry, including occluded parts, from a single RGB image. While diffusion-based reconstructors achieve high accuracy, they typically require many denoising iterations,…

Computer Vision and Pattern Recognition · Computer Science 2026-04-28 Yuta Baba , Keiji Yanai

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…

Computation · Statistics 2012-04-30 Alberto Pasanisi , Shuai Fu , Nicolas Bousquet

We introduce $\texttt{PairFlow}$, a lightweight preprocessing step for training Discrete Flow Models (DFMs) to achieve few-step sampling without requiring a pretrained teacher. DFMs have recently emerged as a new class of generative models…

Machine Learning · Computer Science 2026-05-26 Mingue Park , Jisung Hwang , Seungwoo Yoo , Kyeongmin Yeo , Minhyuk Sung

Flow-matching models have enabled high-quality text-to-speech synthesis, but their iterative sampling process during inference incurs substantial computational cost. Although distillation is widely used to reduce the number of inference…

Sound · Computer Science 2026-02-11 Bin Lin , Peng Yang , Chao Yan , Xiaochen Liu , Wei Wang , Boyong Wu , Pengfei Tan , Xuerui Yang

Discrete diffusion models based on continuous-time Markov chains (CTMCs) have shown strong performance on language and discrete data generation, yet existing approaches typically parameterize the reverse rate matrix monolithically --…

Machine Learning · Computer Science 2026-05-11 Jingyuan Li , Xiaoyi Jiang , Fukang Wen , Wei Liu , Renqian Luo , Yi Zhu , Zuoqiang Shi , Pipi Hu

Generative policies based on diffusion and flow matching achieve strong performance in robotic manipulation by modeling multi-modal human demonstrations. However, their reliance on iterative Ordinary Differential Equation (ODE) integration…

Guidance provides a simple and effective framework for posterior sampling by steering the generation process towards the desired distribution. When modeling discrete data, existing approaches mostly focus on guidance with the first-order…

Machine Learning · Computer Science 2026-04-16 Zhengyan Wan , Yidong Ouyang , Liyan Xie , Fang Fang , Hongyuan Zha , Guang Cheng

Generative models on discrete state-spaces have a wide range of potential applications, particularly in the domain of natural sciences. In continuous state-spaces, controllable and flexible generation of samples with desired properties has…

Machine Learning · Computer Science 2025-03-27 Hunter Nisonoff , Junhao Xiong , Stephan Allenspach , Jennifer Listgarten

Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in…

Machine Learning · Computer Science 2026-02-03 Yuhao Huang , Taos Transue , Shih-Hsin Wang , William Feldman , Hong Zhang , Bao Wang

In robot manipulation, robot learning has become a prevailing approach. However, generative models within this field face a fundamental trade-off between the slow, iterative sampling of diffusion models and the architectural constraints of…

Robotics · Computer Science 2025-12-04 Juyi Sheng , Ziyi Wang , Peiming Li , Mengyuan Liu

We present the statistical method as a direct extension of the mean first-passage time concept to the analysis of molecular dynamics simulation data of a phase transformation. According to the method, the mean first-passage time…

Soft Condensed Matter · Physics 2015-06-18 Anatolii V. Mokshin , Bulat N. Galimzyanov

We propose a unified, few-step generative modeling framework based on \emph{cumulative flow maps} for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a…

Machine Learning · Computer Science 2026-05-06 Zhiqi Li , Duowen Chen , Yuchen Sun , Bo Zhu