[Paper Review] DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models

Cheng Lu, Y. Zhou+4 more|arXiv (Cornell University)|Nov 2, 2022

Generative Adversarial Networks and Image SynthesisComputer Science101 citations

TL;DR

DPM-Solver++ provides a training-free, high-order diffusion ODE solver for guided sampling that achieves high-quality samples in about 15–20 steps, outperforming prior fast solvers for guided tasks.

ABSTRACT

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of DPMs is guided sampling, which usually needs a large guidance scale to obtain the best sample quality. The commonly-used fast sampler for guided sampling is DDIM, a first-order diffusion ODE solver that generally needs 100 to 250 steps for high-quality samples. Although recent works propose dedicated high-order solvers and achieve a further speedup for sampling without guidance, their effectiveness for guided sampling has not been well-tested before. In this work, we demonstrate that previous high-order fast samplers suffer from instability issues, and they even become slower than DDIM when the guidance scale grows large. To further speed up guided sampling, we propose DPM-Solver++, a high-order solver for the guided sampling of DPMs. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matches training data distribution. We further propose a multistep variant of DPM-Solver++ to address the instability issue by reducing the effective step size. Experiments show that DPM-Solver++ can generate high-quality samples within only 15 to 20 steps for guided sampling by pixel-space and latent-space DPMs.

Motivation & Objective

• Motivate the need for faster, high-quality guided sampling in diffusion probabilistic models (DPMs).
• Identify instability and train-test mismatch issues in existing high-order solvers under large guidance scales.
• Propose DPM-Solver++ using data-prediction parameterization, thresholding, and multistep strategies to enable fast, stable guided sampling.
• Demonstrate efficacy across pixel-space and latent-space DPMs with guided sampling.
• Provide training-free solver methods with theoretical convergence guarantees and practical algorithms.

Proposed method

• Solve the diffusion ODE with the data prediction model x_theta rather than the noise prediction model epsilon_theta.
• Develop a high-order solver (DPM-Solver++(2S)) based on a second-order singlestep scheme with Taylor-based integration and analytic integral terms.
• Introduce a second second-order multistep variant (DPM-Solver++(2M)) that reuses previous solutions to reduce function evaluations.
• Incorporate thresholding to keep samples within the training data distribution bounds under large guidance scales.
• Provide Algorithm 1 (2S) and Algorithm 2 (2M) with convergence guarantees, and relate to exponential-integrator frameworks.
• Optionally extend to diffusion SDE formulations (SDE-DPM-Solver++ variants) for complementary solvers.

Experimental results

Research questions

• RQ1 Can a training-free, high-order solver reliably perform guided sampling for DPMs at large guidance scales without instability?
• RQ2 How does parameterizing the ODE with the data-prediction model affect sample quality and stability under guided sampling?
• RQ3 Do multistep strategies improve efficiency and reduce instability compared to singlestep high-order methods?
• RQ4 Is DPM-Solver++ effective across both pixel-space and latent-space DPMs for guided tasks?
• RQ5 How does thresholding interact with high-order guided samplers to mitigate train-test mismatch?

Key findings

• DPM-Solver++ can generate high-quality guided samples in 15–20 steps, outperforming prior fast samplers for guided sampling.
• Using the data prediction model and thresholding mitigates train-test mismatch and improves stability under large guidance scales.
• A second-order multistep variant (2M) offers efficiency gains by reusing previous information and can be slightly better than the singlestep version (2S).
• The approach applies to both pixel-space and latent-space DPMs, demonstrating broad applicability for guided sampling tasks.
• DPM-Solver++ unifies and extends DDIM as its first-order case and provides a training-free alternative with strong empirical performance.