# Zero-Shot Uncertainty Quantification using Diffusion Probabilistic Models

arXiv: https://arxiv.org/abs/2408.04718 · HTML: https://mlsanity.com/paper/2408.04718/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 20 of its 71 references that are in the map.
- First posted on arXiv 8 Aug 2024.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [SegDiff: Image Segmentation with Diffusion Probabilistic Models](https://mlsanity.com/paper/2112.00390/) (2021)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [DiffusionDepth: Diffusion Denoising Approach for Monocular Depth Estimation](https://mlsanity.com/paper/2303.05021/) (2023)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.11833/) (2023)
- [Estimating Epistemic and Aleatoric Uncertainty with a Single Model](https://mlsanity.com/paper/2402.03478/) (2024)
- [Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity](https://mlsanity.com/paper/2405.19166/) (2024)
- [SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models](https://mlsanity.com/paper/2306.14066/) (2023)
- [Deep Ensembles from a Bayesian Perspective](https://mlsanity.com/paper/2105.13283/) (2021)
- [Real-time Inference and Extrapolation via a Diffusion-inspired Temporal Transformer Operator (DiTTO)](https://mlsanity.com/paper/2307.09072/) (2023)
- [Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEs](https://mlsanity.com/paper/2403.10642/) (2024)
- [Strategies for Pretraining Neural Operators](https://mlsanity.com/paper/2406.08473/) (2024)
- [CaFA: Global Weather Forecasting with Factorized Attention on Sphere](https://mlsanity.com/paper/2405.07395/) (2024)
- [Pretraining a Neural Operator in Lower Dimensions](https://mlsanity.com/paper/2407.17616/) (2024)

## Built on by (most cited first, 14 of 14)

- [Generative Latent Neural PDE Solver using Flow Matching](https://mlsanity.com/paper/2503.22600/) (2025)
- [Unifying and extending Diffusion Models through PDEs for solving Inverse Problems](https://mlsanity.com/paper/2504.07437/) (2025)
- [Evidential Uncertainty Estimation for Multi-Modal Trajectory Prediction](https://mlsanity.com/paper/2503.05274/) (2025)
- [Trustworthy image-to-image translation: evaluating uncertainty calibration in unpaired training scenarios](https://mlsanity.com/paper/2501.17570/) (2025)
- [When do World Models Successfully Learn Dynamical Systems?](https://mlsanity.com/paper/2507.04898/) (2025)
- [Using Ensemble Diffusion to Estimate Uncertainty for End-to-End Autonomous Driving](https://mlsanity.com/paper/2506.00560/) (2025)
- [Improved probabilistic regression using diffusion models](https://mlsanity.com/paper/2510.04583/) (2025)
- [Quantifying Epistemic Uncertainty in Diffusion Models](https://mlsanity.com/paper/2602.09170/) (2026)
- [DAV-GSWT: Diffusion-Active-View Sampling for Data-Efficient Gaussian Splatting Wang Tiles](https://mlsanity.com/paper/2602.15355/) (2026)
- [Probabilistic Precipitation Nowcasting with Rectified Flow Transformers](https://mlsanity.com/paper/2605.31204/) (2026)
- [Comparison of Generative Learning Methods for Turbulence Surrogates](https://mlsanity.com/paper/2411.16417/) (2024)
- [Perfecting Depth: Uncertainty-Aware Enhancement of Metric Depth](https://mlsanity.com/paper/2506.04612/) (2025)
- [Coupled Diffusion-Encoder Models for Reconstruction of Flow Fields](https://mlsanity.com/paper/2601.07946/) (2026)
- [DiffUNet^2: Bidirectional Conditional Diffusion for Probabilistic Scientific Spatiotemporal Modeling](https://mlsanity.com/paper/2606.03926/) (2026)

## Abstract (arXiv)

The success of diffusion probabilistic models in generative tasks, such as text-to-image generation, has motivated the exploration of their application to regression problems commonly encountered in scientific computing and various other domains. In this context, the use of diffusion regression models for ensemble prediction is becoming a practice with increasing popularity. Under such background, we conducted a study to quantitatively evaluate the effectiveness of ensemble methods on solving different regression problems using diffusion models. We consider the ensemble prediction of a diffusion model as a means for zero-shot uncertainty quantification, since the diffusion models in our study are not trained with a loss function containing any uncertainty estimation. Through extensive experiments on 1D and 2D data, we demonstrate that ensemble methods consistently improve model prediction accuracy across various regression tasks. Notably, we observed a larger accuracy gain in auto-regressive prediction compared with point-wise prediction, and that enhancements take place in both the mean-square error and the physics-informed loss. Additionally, we reveal a statistical correlation between ensemble prediction error and ensemble variance, offering insights into balancing computational complexity with prediction accuracy and monitoring prediction confidence in practical applications where the ground truth is unknown. Our study provides a comprehensive view of the utility of diffusion ensembles, serving as a useful reference for practitioners employing diffusion models in regression problem-solving.