# A Unified Sampling Framework for Solver Searching of Diffusion Probabilistic Models

arXiv: https://arxiv.org/abs/2312.07243 · HTML: https://mlsanity.com/paper/2312.07243/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 33 of its 39 references that are in the map.
- First posted on arXiv 12 Dec 2023.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [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)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [Population Based Training of Neural Networks](https://mlsanity.com/paper/1711.09846/) (2017)
- [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)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [Regularizing and Optimizing LSTM Language Models](https://mlsanity.com/paper/1708.02182/) (2017)
- [DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics](https://mlsanity.com/paper/2310.13268/) (2023)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)
- [gDDIM: Generalized denoising diffusion implicit models](https://mlsanity.com/paper/2206.05564/) (2022)

## Built on by (most cited first, 14 of 14)

- [ViDiT-Q: Efficient and Accurate Quantization of Diffusion Transformers for Image and Video Generation](https://mlsanity.com/paper/2406.02540/) (2024)
- [Efficient Expert Pruning for Sparse Mixture-of-Experts Language Models: Enhancing Performance and Reducing Inference Costs](https://mlsanity.com/paper/2407.00945/) (2024)
- [Learning to Discretize Denoising Diffusion ODEs](https://mlsanity.com/paper/2405.15506/) (2024)
- [Not All Prompts Are Made Equal: Prompt-based Pruning of Text-to-Image Diffusion Models](https://mlsanity.com/paper/2406.12042/) (2024)
- [AdaNAT: Exploring Adaptive Policy for Token-Based Image Generation](https://mlsanity.com/paper/2409.00342/) (2024)
- [SADA: Stability-guided Adaptive Diffusion Acceleration](https://mlsanity.com/paper/2507.17135/) (2025)
- [S4S: Solving for a Diffusion Model Solver](https://mlsanity.com/paper/2502.17423/) (2025)
- [ENAT: Rethinking Spatial-temporal Interactions in Token-based Image Synthesis](https://mlsanity.com/paper/2411.06959/) (2024)
- [Linear Combination of Saved Checkpoints Makes Consistency and Diffusion Models Better](https://mlsanity.com/paper/2404.02241/) (2024)
- [Towards efficient quantum algorithms for diffusion probabilistic models](https://mlsanity.com/paper/2502.14252/) (2025)
- [Generative Diffusion Model Bootstraps Zero-shot Classification of Fetal Ultrasound Images In Underrepresented African Populations](https://mlsanity.com/paper/2407.20072/) (2024)
- [Colored Noise Diffusion Sampling](https://mlsanity.com/paper/2605.30332/) (2026)
- [AdaGen: Learning Adaptive Policy for Image Synthesis](https://mlsanity.com/paper/2603.06993/) (2026)
- [NI Sampling: Accelerating Discrete Diffusion Sampling by Token Order Optimization](https://mlsanity.com/paper/2604.18471/) (2026)

## Abstract (arXiv)

Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the generation of DPMs usually consumes much time due to the large number of function evaluations (NFE). Though recent works have accelerated the sampling to around 20 steps with high-order solvers, the sample quality with less than 10 NFE can still be improved. In this paper, we propose a unified sampling framework (USF) to study the optional strategies for solver. Under this framework, we further reveal that taking different solving strategies at different timesteps may help further decrease the truncation error, and a carefully designed solver schedule has the potential to improve the sample quality by a large margin. Therefore, we propose a new sampling framework based on the exponential integral formulation that allows free choices of solver strategy at each step and design specific decisions for the framework. Moreover, we propose S3, a predictor-based search method that automatically optimizes the solver schedule to get a better time-quality trade-off of sampling. We demonstrate that S3 can find outstanding solver schedules which outperform the state-of-the-art sampling methods on CIFAR-10, CelebA, ImageNet, and LSUN-Bedroom datasets. Specifically, we achieve 2.69 FID with 10 NFE and 6.86 FID with 5 NFE on CIFAR-10 dataset, outperforming the SOTA method significantly. We further apply S3 to Stable-Diffusion model and get an acceleration ratio of 2×, showing the feasibility of sampling in very few steps without retraining the neural network.