# Accelerating Discrete Diffusion Models with Parallel-In-Time Sampling

arXiv: https://arxiv.org/abs/2607.00773 · HTML: https://mlsanity.com/paper/2607.00773/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 49 of its 68 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 49)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [Diffsound: Discrete Diffusion Model for Text-to-sound Generation](https://mlsanity.com/paper/2207.09983/) (2022)
- [Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling](https://mlsanity.com/paper/2409.02908/) (2024)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [A Reparameterized Discrete Diffusion Model for Text Generation](https://mlsanity.com/paper/2302.05737/) (2023)
- [The Diffusion Duality](https://mlsanity.com/paper/2506.10892/) (2025)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)
- [Dimple: Discrete Diffusion Multimodal Large Language Model with Parallel Decoding](https://mlsanity.com/paper/2505.16990/) (2025)
- [Path Planning for Masked Diffusion Model Sampling](https://mlsanity.com/paper/2502.03540/) (2025)
- [Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Design](https://mlsanity.com/paper/2410.13643/) (2024)
- [The Randomized Midpoint Method for Log-Concave Sampling](https://mlsanity.com/paper/1909.05503/) (2019)
- [Think While You Generate: Discrete Diffusion with Planned Denoising](https://mlsanity.com/paper/2410.06264/) (2024)
- [Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspective](https://mlsanity.com/paper/2412.03487/) (2024)
- [How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework](https://mlsanity.com/paper/2410.03601/) (2024)
- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization](https://mlsanity.com/paper/2402.08095/) (2024)
- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Accelerating Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2402.09970/) (2024)
- [Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel](https://mlsanity.com/paper/2406.00924/) (2024)
- [A Pytorch Reproduction of Masked Generative Image Transformer](https://mlsanity.com/paper/2310.14400/) (2023)

## Built on by (most cited first, 4 of 4)

- [DiffusionGemma Technical Report](https://mlsanity.com/paper/2608.00146/) (2026)
- [Discrete Diffusion Models via Evolving Variational Autoregressive Networks](https://mlsanity.com/paper/2609.27306/) (2026)
- [Counterfactual Probing for Parallel Unmasking with Hidden Forest Structure](https://mlsanity.com/paper/2609.37841/) (2026)
- [Scalable Minimal-Change Learning for Controllable Image Editing](https://mlsanity.com/paper/2610.06021/) (2026)

## Abstract (arXiv)

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 τ-leaping algorithm for absorbing discrete diffusion in a Continuous-Time Markov Chain (CTMC) framework. By leveraging the continuous-time stochastic integral form of the τ-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 τ-leaping under absorbing settings from O(d log S) to O(log (dlog S)· log d) with respect to NFE. Empirically, our method shows consistent acceleration across synthetic and real-data settings. The new sampler achieves at most 7--9× runtime speedup for synthetic distribution, and maintains the same quality with 50% fewer NFE and 1.45--1.86× 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.