# Diffusion Model Guided Sampling with Pixel-Wise Aleatoric Uncertainty Estimation

arXiv: https://arxiv.org/abs/2412.00205 · HTML: https://mlsanity.com/paper/2412.00205/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 37 of its 54 references that are in the map.
- First posted on arXiv 29 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 37)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [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)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium](https://mlsanity.com/paper/1706.08500/) (2017)
- [On the uncertainty of self-supervised monocular depth estimation](https://mlsanity.com/paper/2005.06209/) (2020)
- [Effectively Unbiased FID and Inception Score and where to find them](https://mlsanity.com/paper/1911.07023/) (2019)
- [Can Autonomous Vehicles Identify, Recover From, and Adapt to Distribution Shifts?](https://mlsanity.com/paper/2006.14911/) (2020)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [Bayesian Uncertainty Estimation for Batch Normalized Deep Networks](https://mlsanity.com/paper/1802.06455/) (2018)
- [Improving black-box optimization in VAE latent space using decoder uncertainty](https://mlsanity.com/paper/2107.00096/) (2021)
- [BayesDiff: Estimating Pixel-wise Uncertainty in Diffusion via Bayesian Inference](https://mlsanity.com/paper/2310.11142/) (2023)
- [Bayesian GAN](https://mlsanity.com/paper/1705.09558/) (2017)
- [Training-Free Uncertainty Estimation for Dense Regression: Sensitivity as a Surrogate](https://mlsanity.com/paper/1910.04858/) (2019)
- [Gradient-based Uncertainty for Monocular Depth Estimation](https://mlsanity.com/paper/2208.02005/) (2022)
- [DiffEnc: Variational Diffusion with a Learned Encoder](https://mlsanity.com/paper/2310.19789/) (2023)
- [Multi-conditioned Graph Diffusion for Neural Architecture Search](https://mlsanity.com/paper/2403.06020/) (2024)

## Built on by (most cited first, 20 of 20)

- [Generative Uncertainty in Diffusion Models](https://mlsanity.com/paper/2502.20946/) (2025)
- [Self-Refining Video Sampling](https://mlsanity.com/paper/2601.18577/) (2026)
- [Flow Matching with Uncertainty Quantification and Guidance](https://mlsanity.com/paper/2602.10326/) (2026)
- [Epistemic Generative Adversarial Networks](https://mlsanity.com/paper/2603.18348/) (2026)
- [PAD-Hand: Physics-Aware Diffusion for Hand Motion Recovery](https://mlsanity.com/paper/2603.26068/) (2026)
- [Uncertainty-Aware Likelihood Ratio Estimation for Pixel-Wise Out-of-Distribution Detection](https://mlsanity.com/paper/2508.00587/) (2025)
- [Quantifying Epistemic Uncertainty in Diffusion Models](https://mlsanity.com/paper/2602.09170/) (2026)
- [When Are Two Scores Better Than One? Investigating Ensembles of Diffusion Models](https://mlsanity.com/paper/2601.11444/) (2026)
- [Uncertainty-Aware Distribution-to-Distribution Flow Matching for Scientific Imaging](https://mlsanity.com/paper/2603.21717/) (2026)
- [Spatially Adaptive Noise Injection](https://mlsanity.com/paper/2609.18466/) (2026)
- [LC4-DViT: Land-cover Creation for Land-cover Classification with Deformable Vision Transformer](https://mlsanity.com/paper/2511.22812/) (2025)
- [Inline Critic Steers Image Editing](https://mlsanity.com/paper/2605.12724/) (2026)
- [Uncertainty-Calibrated Diffusion for Reliable 3D Molecular Graph Generation](https://mlsanity.com/paper/2606.01595/) (2026)
- [Uncertainty Estimation for Molecular Diffusion Models](https://mlsanity.com/paper/2606.13451/) (2026)
- [LM-X: Explainable Vision--Language--Action Modeling via Progress, Event, and Uncertainty Prediction](https://mlsanity.com/paper/2608.25757/) (2026)
- [Is your uncertainty map wrong, or is its target? Exact diagnostics for the Tweedie diagonal, and a gradient-free alternative](https://mlsanity.com/paper/2609.33786/) (2026)
- [Generative Uncertainty as a Self-supervised Signal for Semantic Similarity Learning](https://mlsanity.com/paper/2609.35341/) (2026)
- [TRACE: Time-Adaptive Residual Attention Control with Content-Style Decomposition for Training-Free Diffusion Style Transfer](https://mlsanity.com/paper/2610.04922/) (2026)
- [Triggering Generalist Reasoning via Predictive Uncertainty for Dual-System VLA](https://mlsanity.com/paper/2610.05025/) (2026)
- [Posterior Flow Matching](https://mlsanity.com/paper/2610.13994/) (2026)

## Abstract (arXiv)

Despite the remarkable progress in generative modelling, current diffusion models lack a quantitative approach to assess image quality. To address this limitation, we propose to estimate the pixel-wise aleatoric uncertainty during the sampling phase of diffusion models and utilise the uncertainty to improve the sample generation quality. The uncertainty is computed as the variance of the denoising scores with a perturbation scheme that is specifically designed for diffusion models. We then show that the aleatoric uncertainty estimates are related to the second-order derivative of the diffusion noise distribution. We evaluate our uncertainty estimation algorithm and the uncertainty-guided sampling on the ImageNet and CIFAR-10 datasets. In our comparisons with the related work, we demonstrate promising results in filtering out low quality samples. Furthermore, we show that our guided approach leads to better sample generation in terms of FID scores.