# Uncertainty Estimation for Molecular Diffusion Models

arXiv: https://arxiv.org/abs/2606.13451 · HTML: https://mlsanity.com/paper/2606.13451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 23 of its 25 references that are in the map.
- First posted on arXiv 11 Jun 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 23 of 23)

- [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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Understanding Hallucinations in Diffusion Models through Mode Interpolation](https://mlsanity.com/paper/2406.09358/) (2024)
- [Geometry-Complete Diffusion for 3D Molecule Generation and Optimization](https://mlsanity.com/paper/2302.04313/) (2023)
- [BayesDiff: Estimating Pixel-wise Uncertainty in Diffusion via Bayesian Inference](https://mlsanity.com/paper/2310.11142/) (2023)
- [Generative Uncertainty in Diffusion Models](https://mlsanity.com/paper/2502.20946/) (2025)
- [Shedding Light on Large Generative Networks: Estimating Epistemic Uncertainty in Diffusion Models](https://mlsanity.com/paper/2406.18580/) (2024)
- [Diffusion Model Guided Sampling with Pixel-Wise Aleatoric Uncertainty Estimation](https://mlsanity.com/paper/2412.00205/) (2024)
- [Equivariant Neural Diffusion for Molecule Generation](https://mlsanity.com/paper/2506.10532/) (2025)
- [Adaptive Inference-Time Scaling via Cyclic Diffusion Search](https://mlsanity.com/paper/2505.14036/) (2025)
- [Identity Curvature Laplace Approximation for Improved Out-of-Distribution Detection](https://mlsanity.com/paper/2312.10464/) (2023)

## Abstract (arXiv)

Diffusion models have seen wide adoption for 3D molecular generation, yet they offer no principled signal of when a generated molecule is likely to be of low quality. We propose a post-hoc method for estimating per-sample uncertainty in pretrained molecular diffusion models. Building on a Laplace approximation of the denoising network, we measure the variability of the noise prediction across the generation trajectory. Empirically, we show that the resulting uncertainty score is informative of sample quality, exhibiting a negative correlation with established sample-level quality metrics. We further study how the proposed uncertainty score can be used to filter generated samples, improving model performance via test-time scaling.