# Diffusion Sampling Correction via Approximately 10 Parameters

arXiv: https://arxiv.org/abs/2411.06503 · HTML: https://mlsanity.com/paper/2411.06503/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 42 of its 54 references that are in the map.
- First posted on arXiv 10 Nov 2024.

## Placed in

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

## Builds on (most cited first, 30 of 42)

- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [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)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [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)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Patch n' Pack: NaViT, a Vision Transformer for any Aspect Ratio and Resolution](https://mlsanity.com/paper/2307.06304/) (2023)
- [FreeU: Free Lunch in Diffusion U-Net](https://mlsanity.com/paper/2309.11497/) (2023)
- [DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics](https://mlsanity.com/paper/2310.13268/) (2023)
- [Cache Me if You Can: Accelerating Diffusion Models through Block Caching](https://mlsanity.com/paper/2312.03209/) (2023)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)

## Built on by (most cited first, 3 of 3)

- [Three Creates All: You Only Sample 3 Steps](https://mlsanity.com/paper/2603.22375/) (2026)
- [TraceSampler: Making Sampling Errors Predictable and Correctable for Accelerated Generative Sampling](https://mlsanity.com/paper/2610.14332/) (2026)
- [Tikhonov-Stabilized Bezier Representation Forecasting for Training-free Diffusion Acceleration](https://mlsanity.com/paper/2610.16448/) (2026)

## Abstract (arXiv)

While powerful for generation, Diffusion Probabilistic Models (DPMs) face slow sampling challenges, for which various distillation-based methods have been proposed. However, they typically require significant additional training costs and model parameter storage, limiting their practicality. In this work, we propose PCA-based Adaptive Search (PAS), which optimizes existing solvers for DPMs with minimal additional costs. Specifically, we first employ PCA to obtain a few basis vectors to span the high-dimensional sampling space, which enables us to learn just a set of coordinates to correct the sampling direction; furthermore, based on the observation that the cumulative truncation error exhibits an ``S"-shape, we design an adaptive search strategy that further enhances the sampling efficiency and reduces the number of stored parameters to approximately 10. Extensive experiments demonstrate that PAS can significantly enhance existing fast solvers in a plug-and-play manner with negligible costs. E.g., on CIFAR10, PAS optimizes DDIM's FID from 15.69 to 4.37 (NFE=10) using only 12 parameters and sub-minute training on a single A100 GPU. Code is available at https://github.com/onefly123/PAS.