# On Inference Stability for Diffusion Models

arXiv: https://arxiv.org/abs/2312.12431 · HTML: https://mlsanity.com/paper/2312.12431/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 22 of its 27 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)
- [Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models](https://mlsanity.com/paper/2206.07309/) (2022)
- [Lookahead Diffusion Probabilistic Models for Refining Mean Estimation](https://mlsanity.com/paper/2304.11312/) (2023)

## Built on by (most cited first, 4 of 4)

- [Improved Training Technique for Shortcut Models](https://mlsanity.com/paper/2510.21250/) (2025)
- [CGCE: Classifier-Guided Concept Erasure in Generative Models](https://mlsanity.com/paper/2511.05865/) (2025)
- [Cross-Space Distillation: Teaching One-Step Students with Modern Diffusion Teachers](https://mlsanity.com/paper/2606.32020/) (2026)
- [Artificial Immunofluorescence in a Flash: Rapid Synthetic Imaging from Brightfield Through Residual Diffusion](https://mlsanity.com/paper/2407.17882/) (2024)

## Abstract (arXiv)

Denoising Probabilistic Models (DPMs) represent an emerging domain of generative models that excel in generating diverse and high-quality images. However, most current training methods for DPMs often neglect the correlation between timesteps, limiting the model's performance in generating images effectively. Notably, we theoretically point out that this issue can be caused by the cumulative estimation gap between the predicted and the actual trajectory. To minimize that gap, we propose a novel textitsequence-aware loss that aims to reduce the estimation gap to enhance the sampling quality. Furthermore, we theoretically show that our proposed loss function is a tighter upper bound of the estimation loss in comparison with the conventional loss in DPMs. Experimental results on several benchmark datasets including CIFAR10, CelebA, and CelebA-HQ consistently show a remarkable improvement of our proposed method regarding the image generalization quality measured by FID and Inception Score compared to several DPM baselines. Our code and pre-trained checkpoints are available at urlhttps://github.com/VinAIResearch/SA-DPM.