# Enhanced Diffusion Sampling via Extrapolation with Multiple ODE Solutions

arXiv: https://arxiv.org/abs/2504.01855 · HTML: https://mlsanity.com/paper/2504.01855/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [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)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [ModelScope Text-to-Video Technical Report](https://mlsanity.com/paper/2308.06571/) (2023)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [MagicVideo: Efficient Video Generation With Latent Diffusion Models](https://mlsanity.com/paper/2211.11018/) (2022)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [GENIE: Higher-Order Denoising Diffusion Solvers](https://mlsanity.com/paper/2210.05475/) (2022)
- [Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models](https://mlsanity.com/paper/2206.07309/) (2022)
- [Lookahead Diffusion Probabilistic Models for Refining Mean Estimation](https://mlsanity.com/paper/2304.11312/) (2023)
- [On Accelerating Diffusion-Based Sampling Process via Improved Integration Approximation](https://mlsanity.com/paper/2304.11328/) (2023)
- [Observation-Guided Diffusion Probabilistic Models](https://mlsanity.com/paper/2310.04041/) (2023)

## Built on by (most cited first, 8 of 8)

- [Understanding Sampler Stochasticity in Training Diffusion Models for RLHF](https://mlsanity.com/paper/2510.10767/) (2025)
- [Tortoise and Hare Guidance: Accelerating Diffusion Model Inference with Multirate Integration](https://mlsanity.com/paper/2511.04117/) (2025)
- [Few-Step Diffusion Sampling Through Instance-Aware Discretizations](https://mlsanity.com/paper/2603.17671/) (2026)
- [Rethinking FID Through the Geometry of the Reference Dataset](https://mlsanity.com/paper/2605.29335/) (2026)
- [MM-TRELLIS: Point-Cloud Guided Multi-Modal 3D Vehicle Generation in Autonomous Driving](https://mlsanity.com/paper/2606.24301/) (2026)
- [Asymptotic Preservation and Uniform Accuracy of Diffusion and Flow-Matching Samplers](https://mlsanity.com/paper/2607.04113/) (2026)
- [D2PO: Optimizing Diffusion Samplers via Dynamic Preference](https://mlsanity.com/paper/2607.06609/) (2026)
- [What Does Fr'echet Distance Measure? A Directional Decomposition](https://mlsanity.com/paper/2610.05518/) (2026)

## Abstract (arXiv)

Diffusion probabilistic models (DPMs), while effective in generating high-quality samples, often suffer from high computational costs due to their iterative sampling process. To address this, we propose an enhanced ODE-based sampling method for DPMs inspired by Richardson extrapolation, which reduces numerical error and improves convergence rates. Our method, RX-DPM, leverages multiple ODE solutions at intermediate time steps to extrapolate the denoised prediction in DPMs. This significantly enhances the accuracy of estimations for the final sample while maintaining the number of function evaluations (NFEs). Unlike standard Richardson extrapolation, which assumes uniform discretization of the time grid, we develop a more general formulation tailored to arbitrary time step scheduling, guided by local truncation error derived from a baseline sampling method. The simplicity of our approach facilitates accurate estimation of numerical solutions without significant computational overhead, and allows for seamless and convenient integration into various DPMs and solvers. Additionally, RX-DPM provides explicit error estimates, effectively demonstrating the faster convergence as the leading error term's order increases. Through a series of experiments, we show that the proposed method improves the quality of generated samples without requiring additional sampling iterations.