# Variance-Reduction Guidance: Sampling Trajectory Optimization for Diffusion Models

arXiv: https://arxiv.org/abs/2510.21792 · HTML: https://mlsanity.com/paper/2510.21792/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [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)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)
- [AutoDiffusion: Training-Free Optimization of Time Steps and Architectures for Automated Diffusion Model Acceleration](https://mlsanity.com/paper/2309.10438/) (2023)
- [Accelerating Guided Diffusion Sampling with Splitting Numerical Methods](https://mlsanity.com/paper/2301.11558/) (2023)
- [On Accelerating Diffusion-Based Sampling Process via Improved Integration Approximation](https://mlsanity.com/paper/2304.11328/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Gaussian Perspective for Distributional Discrepancy in Generative Diffusion Models](https://mlsanity.com/paper/2601.13602/) (2026)

## Abstract (arXiv)

Diffusion models have become emerging generative models. Their sampling process involves multiple steps, and in each step the models predict the noise from a noisy sample. When the models make prediction, the output deviates from the ground truth, and we call such a deviation as textitprediction error. The prediction error accumulates over the sampling process and deteriorates generation quality. This paper introduces a novel technique for statistically measuring the prediction error and proposes the Variance-Reduction Guidance (VRG) method to mitigate this error. VRG does not require model fine-tuning or modification. Given a predefined sampling trajectory, it searches for a new trajectory which has the same number of sampling steps but produces higher quality results. VRG is applicable to both conditional and unconditional generation. Experiments on various datasets and baselines demonstrate that VRG can significantly improve the generation quality of diffusion models. Source code is available at https://github.com/shifengxu/VRG.