# Distilling ODE Solvers of Diffusion Models into Smaller Steps

arXiv: https://arxiv.org/abs/2309.16421 · HTML: https://mlsanity.com/paper/2309.16421/

## Key facts

- Cited by 11 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 63 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Placed in

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

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [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)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)

## Built on by (most cited first, 11 of 11)

- [Simple ReFlow: Improved Techniques for Fast Flow Models](https://mlsanity.com/paper/2410.07815/) (2024)
- [Attend to Not Attended: Structure-then-Detail Token Merging for Post-training DiT Acceleration](https://mlsanity.com/paper/2505.11707/) (2025)
- [Distilling Parallel Gradients for Fast ODE Solvers of Diffusion Models](https://mlsanity.com/paper/2507.14797/) (2025)
- [Optimizing for the Shortest Path in Denoising Diffusion Model](https://mlsanity.com/paper/2503.03265/) (2025)
- [DyWeight: Dynamic Gradient Weighting for Few-Step Diffusion Sampling](https://mlsanity.com/paper/2603.11607/) (2026)
- [Few-Step Diffusion Sampling Through Instance-Aware Discretizations](https://mlsanity.com/paper/2603.17671/) (2026)
- [Image Diffusion Preview with Consistency Solver](https://mlsanity.com/paper/2512.13592/) (2025)
- [Parallel Diffusion Solver via Residual Dirichlet Policy Optimization](https://mlsanity.com/paper/2512.22796/) (2025)
- [Align Your Tangent: Training Better Consistency Models via Manifold-Aligned Tangents](https://mlsanity.com/paper/2510.00658/) (2025)
- [GAS: Improving Discretization of Diffusion ODEs via Generalized Adversarial Solver](https://mlsanity.com/paper/2510.17699/) (2025)
- [Learning to Solve Generative ODEs Beyond the Linear Span](https://mlsanity.com/paper/2606.08672/) (2026)

## Abstract (arXiv)

Abstract Diffusion models have recently gained prominence as a novel category of generative models. Despite their success, these models face a notable drawback in terms of slow sampling speeds, requiring a high number of function evaluations (NFE) in the order of hundreds or thousands. In response, both learning-free and learning-based sampling strategies have been explored to expedite the sampling process. Learning-free sampling employs various ordinary differential equation (ODE) solvers based on the formulation of diffusion ODEs. However, it encounters challenges in faithfully tracking the true sampling trajectory, particularly for small NFE. Conversely, learning-based sampling methods, such as knowledge distillation, demand extensive additional training, limiting their practical applicability. To overcome these limitations, we introduce Distilled-ODE solvers (D-ODE solvers), a straightforward distillation approach grounded in ODE solver formulations. Our method seamlessly integrates the strengths of both learning-free and learning-based sampling. D-ODE solvers are constructed by introducing a single parameter adjustment to existing ODE solvers. Furthermore, we optimize D-ODE solvers with smaller steps using knowledge distillation from ODE solvers with larger steps across a batch of samples. Comprehensive experiments demonstrate the superior performance of D-ODE solvers compared to existing ODE solvers, including DDIM, PNDM, DPM-Solver, DEIS, and EDM, particularly in scenarios with fewer NFE. Notably, our method incurs negligible computational overhead compared to previous distillation techniques, facilitating straightforward and rapid integration with existing samplers. Qualitative analysis reveals that D-ODE solvers not only enhance image quality but also faithfully follow the target ODE trajectory.