DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps
Cheng LuYuhao ZhouFan BaoJianfei ChenChongxuan LiJun Zhu
Proposes DPM-Solver, a dedicated high-order ODE solver that accelerates diffusion model sampling to just 10 to 20 steps without retraining, achieving up to a 16-fold speedup while maintaining high generation quality.
Diffusion probabilistic models deliver high-quality generation across images, video, and other domains, yet their adoption is limited by slow sampling that requires hundreds or thousands of sequential neural-network evaluations. The article addresses this bottleneck by reframing sampling as the solution of a diffusion ordinary differential equation and exploiting its semi-linear structure.
The authors derive an exact formulation of the diffusion ODE solution that computes the linear term analytically and reduces the remaining task to approximating an exponentially weighted integral of the noise-prediction network. From this formulation they construct DPM-Solver, a family of first-, second-, and third-order solvers with guaranteed convergence order that requires no retraining and works for both continuous- and discrete-time models.
Experiments on CIFAR-10, CelebA 64×64, ImageNet, and LSUN show that DPM-Solver produces samples with competitive FID scores in only 10–20 function evaluations, delivering a 4- to 16-fold speedup over prior training-free methods while matching or exceeding the quality of far slower baselines. The method also supports conditional sampling with classifier guidance.
These results indicate that high-fidelity generation from pretrained diffusion models can now be performed in real time on modest hardware, lowering barriers to deployment in production pipelines. Practitioners should adopt DPM-Solver for sampling workloads that tolerate roughly ten network evaluations; when even fewer steps are needed, progressive distillation remains an option at the cost of additional training.
The main limitations are that the solver is tuned for sampling rather than likelihood evaluation and that the underlying models are still slower than single-step GANs for real-time applications. Results rest on standard benchmarks and fixed random seeds; broader validation across tasks and hardware would increase confidence before large-scale deployment.
- Paper: Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song et al. (2021). It introduces the continuous-time score-based SDE framework and the deterministic probability flow ODE that DPM-Solver analytically formulates and solves.
- Paper: Denoising Diffusion Implicit Models, Jiaming Song et al. (2021). It establishes the non-Markovian deterministic sampling trajectory (DDIM) that provides the foundational accelerated baseline and discretization perspective for diffusion ODE solvers.
- Paper: Denoising Diffusion Probabilistic Models, Jonathan Ho et al. (2020). It provides the core denoising diffusion probabilistic model formulation and noise-prediction network parameterization utilized throughout the paper.
- Paper: Diffusion Models Beat GANs on Image Synthesis, Prafulla Dhariwal et al. (2021). It develops classifier guidance for diffusion models, which DPM-Solver explicitly adapts and supports during fast ODE sampling.
- Paper: Improved Denoising Diffusion Probabilistic Models, Alex Nichol et al. (2021). It introduces improved noise schedules and accelerated sampling strategies for discrete-time diffusion models that motivate continuous-time ODE solver formulations.
- Paper: Variational Diffusion Models, Diederik P. Kingma et al. (2021). It presents the signal-to-noise ratio parameterization and continuous-time perspective underlying the exact semi-linear ODE formulation used in DPM-Solver.
- Paper: Neural Ordinary Differential Equations, Ricky T. Q. Chen et al. (2018). It establishes the continuous-depth Neural ODE paradigm and numerical integration techniques that underpin treating diffusion sampling as solving an ordinary differential equation.
- Paper: Elucidating the Design Space of Diffusion-Based Generative Models, Tero Karras et al. (2022). It systematically analyzes the diffusion ODE design space and proposes tailored second-order Heun integrators alongside optimal noise schedules for efficient sampling.
- Paper: Consistency Models, Yang Song et al. (2023). It builds directly upon the probability flow ODE trajectories of diffusion models to enable ultra-fast one- and few-step sampling through consistency training and distillation.
- Paper: Flow Matching for Generative Modeling, Yaron Lipman et al. (2023). It generalizes continuous flow modeling using optimal transport vector fields that yield straighter ODE integration paths for even faster few-step numerical generation.
- Paper: Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow, Xingchao Liu et al. (2023). It straightens generative ODE trajectories via reflow iterations, reducing the number of solver steps required to reach target data distributions down to single-step inference.
- Paper: Mean Flows for One-step Generative Modeling, Zhengyang Geng et al. (2025). It extends continuous flow and ODE formulation ideas by learning interval-averaged velocity fields to enable high-quality generation in a single network evaluation.
- Paper: A Mathematical Introduction to Diffusion Models, Jianfeng Lu (2026). It provides a rigorous mathematical synthesis and error decomposition of score-based continuous and discrete sampling dynamics, placing high-order solvers in theoretical context.
