cs.LGJun 23, 2026

A Time-Reparameterized Cumulative Intensity Extrapolation Sampler for Discrete Flow Matching

Authors: Feiyang Fu, Hehe Fan

Abstract

Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics. In practice, sampling for DFM commonly employs discretizations such as ττ-leaping, yet efficient sampling methods under a limited number of function evaluations (NFE) remain less studied. To address this gap, we propose the Time-Reparameterized Cumulative Intensity Extrapolation (TR-CIE) sampler, which aims to improve sampling quality when function evaluations are restricted. TR-CIE consists of two components. First, a schedule-based time reparameterization rescales the time grid according to the noise schedule. Under standard factorized DFM rate parameterizations, this transformation of variables absorbs the schedule-dependent growth term and mitigates stiffness near the terminal sampling stage. Second, we introduce a cumulative-intensity extrapolation updating rule. By reusing cached model outputs from the previous step as a history term, this improves the approximation of stepwise cumulative intensities on the resulting non-uniform time grid. We provide a theoretical analysis that bounds the local approximation error of cumulative intensities and establishes convergence results. The resulting sampler requires one NFE per step and introduces no additional model evaluations compared to the standard ττ-leaping sampler. Extensive experiments on synthetic tasks, text generation, and text-to-image benchmarks demonstrate that our method improves sampling quality under limited NFE.

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Jul 1, 2026cs.LG

Accelerating Discrete Diffusion Models with Parallel-In-Time Sampling

Discrete diffusion models are widely used for learning and generating discrete distributions. As the generation process is inherently sequential, the acceleration of sampling is of significant importance. In this work, we parallelize the mainstream ττ-leaping algorithm for absorbing discrete diffusion in a Continuous-Time Markov Chain (CTMC) framework. By leveraging the continuous-time stochastic integral form of the ττ-leaping algorithm and the Picard iteration method, we achieve parallel-in-time sampling acceleration and provide a proof of exponential-factorial convergence for our algorithm. We improve the overall time complexity of ττ-leaping under absorbing settings from O(dlog⁡S){\mathcal{O}}(d \log S) to O(log⁡(dlog⁡S)⋅log⁡d){\mathcal{O}}(\log (d\log S)\cdot \log d) with respect to NFE. Empirically, our method shows consistent acceleration across synthetic and real-data settings. The new sampler achieves at most 77--9×9\times runtime speedup for synthetic distribution, and maintains the same quality with 50%50\% fewer NFE and 1.451.45--1.86×1.86\times runtime speedups in image/text tasks on a single GPU. Our research expands the potential of discrete diffusion models for efficient parallel inference, with broader implications for applications such as molecular structure and language generation.
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Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions

Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution μ1μ_1 from samples drawn from a source distribution μ0μ_0. This framework relies on a fixed coupling between μ0μ_0 and μ1μ_1, and on a deterministic or stochastic bridge to define an interpolating process between the two distributions. The time marginals of this process can then be approximately sampled by estimating the transition rates, or more generally the generator, of its Markovian projection. This framework has recently been extended to the case of discrete source and target distributions, under the name Discrete Flow Matching (DFM). However, theoretical guarantees for such models remain scarce. In this paper, we study two DFM models on Zmd={0,…,m−1}d\mathbb{Z}_m^d = \{0,\ldots,m-1\}^d, sampled through time discretization, and derive non-asymptotic associated bounds for both of them. In contrast to previous work, we establish non-asymptotic bounds in Kullback--Leibler divergence for the early-stopped version of the target distribution. We also derive explicit convergence guarantees in total variation distance with respect to the true target distribution. Importantly, these bounds rely only on an approximation error assumption, relaxing standard score assumptions used in earlier works, while also yielding improved dependence on the vocabulary size mm and the dimension dd.
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