# Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference

arXiv: https://arxiv.org/abs/2405.16387 · HTML: https://mlsanity.com/paper/2405.16387/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- First posted on arXiv 26 May 2024.

## Placed in

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

## Built on by (most cited first, 22 of 22)

- [Provable Acceleration for Diffusion Models under Minimal Assumptions](https://mlsanity.com/paper/2410.23285/) (2024)
- [Minimax Optimality of the Probability Flow ODE for Diffusion Models](https://mlsanity.com/paper/2503.09583/) (2025)
- [Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixtures](https://mlsanity.com/paper/2504.05300/) (2025)
- [Instance-dependent Convergence Theory for Diffusion Models](https://mlsanity.com/paper/2410.13738/) (2024)
- [On the Feature Learning in Diffusion Models](https://mlsanity.com/paper/2412.01021/) (2024)
- [Discrete Diffusion Models: Novel Analysis and New Sampler Guarantees](https://mlsanity.com/paper/2509.16756/) (2025)
- [Optimal Convergence Analysis of DDPM for General Distributions](https://mlsanity.com/paper/2510.27562/) (2025)
- [High-accuracy sampling for diffusion models and log-concave distributions](https://mlsanity.com/paper/2602.01338/) (2026)
- [Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers](https://mlsanity.com/paper/2410.14237/) (2024)
- [High-accuracy and dimension-free sampling with diffusions](https://mlsanity.com/paper/2601.10708/) (2026)
- [Almost Linear Convergence under Minimal Score Assumptions: Quantized Transition Diffusion](https://mlsanity.com/paper/2505.21892/) (2025)
- [Fast Score-Based Sampling via Log-Concave Reductions](https://mlsanity.com/paper/2512.24152/) (2025)
- [On Efficiency-Effectiveness Trade-off of Diffusion-based Recommenders](https://mlsanity.com/paper/2510.17245/) (2025)
- [Multi-Step Consistency Models: Fast Generation with Theoretical Guarantees](https://mlsanity.com/paper/2505.01049/) (2025)
- [Denoising growth complexity: Data geometry and certified schedules for diffusion sampling](https://mlsanity.com/paper/2607.26285/) (2026)
- [On the Collapse Errors Induced by the Deterministic Sampler for Diffusion Models](https://mlsanity.com/paper/2508.16154/) (2025)
- [From Scores to Gibbs Correctors: Accelerating Uniform-Rate Discrete Diffusion Models](https://mlsanity.com/paper/2605.27352/) (2026)
- [Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices](https://mlsanity.com/paper/2606.23627/) (2026)
- [Capturing Conditional Dependence via Auto-regressive Diffusion Models](https://mlsanity.com/paper/2504.21314/) (2025)
- [Are First-Order Diffusion Samplers Really Slower? A Fast Forward-Value Approach](https://mlsanity.com/paper/2512.24927/) (2025)
- [Breaking the Bottlenecks: Scalable Diffusion Models for 3D Molecular Generation](https://mlsanity.com/paper/2601.08963/) (2026)
- [Latent Shadows: The Gaussian-Discrete Duality in Masked Diffusion](https://mlsanity.com/paper/2602.00792/) (2026)

## Abstract (arXiv)

To generate data from trained diffusion models, most inference algorithms, such as DDPM, DDIM, and other variants, rely on discretizing the reverse SDEs or their equivalent ODEs. In this paper, we view such approaches as decomposing the entire denoising diffusion process into several segments, each corresponding to a reverse transition kernel (RTK) sampling subproblem. Specifically, DDPM uses a Gaussian approximation for the RTK, resulting in low per-subproblem complexity but requiring a large number of segments (i.e., subproblems), which is conjectured to be inefficient. To address this, we develop a general RTK framework that enables a more balanced subproblem decomposition, resulting in tilde O(1) subproblems, each with strongly log-concave targets. We then propose leveraging two fast sampling algorithms, the Metropolis-Adjusted Langevin Algorithm (MALA) and Underdamped Langevin Dynamics (ULD), for solving these strongly log-concave subproblems. This gives rise to the RTK-MALA and RTK-ULD algorithms for diffusion inference. In theory, we further develop the convergence guarantees for RTK-MALA and RTK-ULD in total variation (TV) distance: RTK-ULD can achieve ε target error within tildemathcal O(d1/2ε-1) under mild conditions, and RTK-MALA enjoys a O(d2log(d/ε)) convergence rate under slightly stricter conditions. These theoretical results surpass the state-of-the-art convergence rates for diffusion inference and are well supported by numerical experiments.