# Boosting Diffusion Models with an Adaptive Momentum Sampler

arXiv: https://arxiv.org/abs/2308.11941 · HTML: https://mlsanity.com/paper/2308.11941/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 29 of its 45 references that are in the map.
- First posted on arXiv 23 Aug 2023.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Conditional Image Synthesis With Auxiliary Classifier GANs](https://mlsanity.com/paper/1610.09585/) (2016)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018)
- [Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation](https://mlsanity.com/paper/2106.05527/) (2021)
- [Diffusion Action Segmentation](https://mlsanity.com/paper/2303.17959/) (2023)
- [Variants of RMSProp and Adagrad with Logarithmic Regret Bounds](https://mlsanity.com/paper/1706.05507/) (2017)
- [Entropy-driven Sampling and Training Scheme for Conditional Diffusion Generation](https://mlsanity.com/paper/2206.11474/) (2022)
- [On Positive-Unlabeled Classification in GAN](https://mlsanity.com/paper/2002.01136/) (2020)
- [ControlVAE: Tuning, Analytical Properties, and Performance Analysis](https://mlsanity.com/paper/2011.01754/) (2020)
- [PSEUDo: Interactive Pattern Search in Multivariate Time Series with Locality-Sensitive Hashing and Relevance Feedback](https://mlsanity.com/paper/2104.14962/) (2021)

## Built on by (most cited first, 6 of 6)

- [Boosting Diffusion Models with Moving Average Sampling in Frequency Domain](https://mlsanity.com/paper/2403.17870/) (2024)
- [Unmasking Bias in Diffusion Model Training](https://mlsanity.com/paper/2310.08442/) (2023)
- [Unleashing High-Quality Image Generation in Diffusion Sampling Using Second-Order Levenberg-Marquardt-Langevin](https://mlsanity.com/paper/2505.24222/) (2025)
- [Enhancing Diffusion Model Stability for Image Restoration via Gradient Management](https://mlsanity.com/paper/2507.06656/) (2025)
- [Score-based Generative Models with Adaptive Momentum](https://mlsanity.com/paper/2405.13726/) (2024)
- [SynBoost: A Synergistic Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2506.13058/) (2025)

## Abstract (arXiv)

Diffusion probabilistic models (DPMs) have been shown to generate high-quality images without the need for delicate adversarial training. However, the current sampling process in DPMs is prone to violent shaking. In this paper, we present a novel reverse sampler for DPMs inspired by the widely-used Adam optimizer. Our proposed sampler can be readily applied to a pre-trained diffusion model, utilizing momentum mechanisms and adaptive updating to smooth the reverse sampling process and ensure stable generation, resulting in outputs of enhanced quality. By implicitly reusing update directions from early steps, our proposed sampler achieves a better balance between high-level semantics and low-level details. Additionally, this sampler is flexible and can be easily integrated into pre-trained DPMs regardless of the sampler used during training. Our experimental results on multiple benchmarks demonstrate that our proposed reverse sampler yields remarkable improvements over different baselines. We will make the source code available.