# DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models

arXiv: https://arxiv.org/abs/2211.01095 · HTML: https://mlsanity.com/paper/2211.01095/

## Key facts

- Cited by 938 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 43 of its 80 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Placed in

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

## Builds on (most cited first, 30 of 43)

- [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)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (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)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [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)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)

## Built on by (most cited first, 30 of 938)

- [IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2308.06721/) (2023)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [RDT-1B: a Diffusion Foundation Model for Bimanual Manipulation](https://mlsanity.com/paper/2410.07864/) (2024)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [SANA: Efficient High-Resolution Image Synthesis with Linear Diffusion Transformers](https://mlsanity.com/paper/2410.10629/) (2024)
- [Composer: Creative and Controllable Image Synthesis with Composable Conditions](https://mlsanity.com/paper/2302.09778/) (2023)
- [Infinity: Scaling Bitwise AutoRegressive Modeling for High-Resolution Image Synthesis](https://mlsanity.com/paper/2412.04431/) (2024)
- [Preserve Your Own Correlation: A Noise Prior for Video Diffusion Models](https://mlsanity.com/paper/2305.10474/) (2023)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [Timestep Embedding Tells: It's Time to Cache for Video Diffusion Model](https://mlsanity.com/paper/2411.19108/) (2024)
- [SDXL-Lightning: Progressive Adversarial Diffusion Distillation](https://mlsanity.com/paper/2402.13929/) (2024)
- [Mix-of-Show: Decentralized Low-Rank Adaptation for Multi-Concept Customization of Diffusion Models](https://mlsanity.com/paper/2305.18292/) (2023)
- [Text2Room: Extracting Textured 3D Meshes from 2D Text-to-Image Models](https://mlsanity.com/paper/2303.11989/) (2023)
- [LLM-grounded Diffusion: Enhancing Prompt Understanding of Text-to-Image Diffusion Models with Large Language Models](https://mlsanity.com/paper/2305.13655/) (2023)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [DiffusionNFT: Online Diffusion Reinforcement with Forward Process](https://mlsanity.com/paper/2509.16117/) (2025)
- [VideoPhy: Evaluating Physical Commonsense for Video Generation](https://mlsanity.com/paper/2406.03520/) (2024)
- [MM-Diffusion: Learning Multi-Modal Diffusion Models for Joint Audio and Video Generation](https://mlsanity.com/paper/2212.09478/) (2022)
- [SnapFusion: Text-to-Image Diffusion Model on Mobile Devices within Two Seconds](https://mlsanity.com/paper/2306.00980/) (2023)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Deep Compression Autoencoder for Efficient High-Resolution Diffusion Models](https://mlsanity.com/paper/2410.10733/) (2024)

## Abstract (arXiv)

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.