Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Estimating Epistemic and Aleatoric Uncertainty with a Single Model
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Proposes HyperDM, a Bayesian hyper-network that generates diffusion model weights, giving epistemic and aleatoric uncertainty estimates from a single model for CT reconstruction and weather forecasting.
Problem
Estimating epistemic and aleatoric uncertainty for inverse problems in high-stakes settings like medical imaging and weather forecasting is expensive because deep ensembles require training many large models.
Approach
Combine a conditional diffusion model with a Bayesian hyper-network that maps random noise to diffusion model weights; sampling M weights and N diffusion samples per weight yields a predictive distribution decomposed via the law of total variance, trained as a single model.
Key results
- On LUNA16, HyperDM achieves PSNR 35.16 dB and CRPS 0.01 versus DPS-UQ 34.95 dB and MC-Dropout 30.25 dB.
- On ERA5, HyperDM achieves SSIM 0.95, PSNR 33.15 dB, CRPS 0.012, slightly above DPS-UQ (32.83 dB).
- Training a 10-member DPS-UQ ensemble takes 441.09 minutes versus 48.53 minutes for HyperDM on LUNA16 (MC-Dropout 47.03).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace MC-Dropout with HyperDM | Attention U-Net uncertainty estimation · LUNA16 test | PSNR (dB): 30.25 -> 35.16 | Helped |
| replace DPS-UQ with HyperDM | Attention U-Net uncertainty estimation · LUNA16 test | PSNR (dB): 34.95 -> 35.16 | Helped |
| replace DPS-UQ with HyperDM | Attention U-Net uncertainty estimation · LUNA16 test | SSIM: 0.89 -> 0.87 | Hurt |
| replace DPS-UQ with HyperDM | Attention U-Net uncertainty estimation · LUNA16 test | CRPS: 0.01 -> 0.01 | No clear effect |
| replace MC-Dropout with HyperDM | Attention U-Net uncertainty estimation · ERA5 test | PSNR (dB): 31.34 -> 33.15 | Helped |
| replace DPS-UQ with HyperDM | Attention U-Net uncertainty estimation · ERA5 test | PSNR (dB): 32.83 -> 33.15 | Helped |
| replace MC-Dropout with HyperDM | Attention U-Net uncertainty estimation · ERA5 test | CRPS: 0.034 -> 0.012 | Helped |
| replace DPS-UQ with HyperDM | Attention U-Net uncertainty estimation · ERA5 test | SSIM: 0.94 -> 0.95 | Helped |
| replace DPS-UQ with HyperDM | Attention U-Net uncertainty estimation · ERA5 test | CRPS: 0.013 -> 0.012 | Helped |
| increase the number of sampled hyper-network weights M (ablation) | HyperDM · OOD temperature forecasting | epistemic uncertainty localization: M={2, 4, 8, 16} | Helped |
| increase the number of diffusion predictions N per sampled weight (ablation) | HyperDM · OOD temperature forecasting | aleatoric uncertainty smoothness: N={2, 4, 8, 16} | Helped |
| aggregate ensemble predictions with the median instead of the mean (ablation) | HyperDM · ERA5 test | PSNR (dB): 32.93 -> 33.06 | Helped |
Surprising findings
- HyperDM's prediction quality was higher than the 10-member deep ensemble baseline DPS-UQ in several metrics despite using a single trained model.
- BNN baseline gave worse PSNR than HyperDM at most dataset sizes, and was only better at the smallest dataset (100 samples) on PSNR.
Limitations
- Diffusion model inference is slow due to iterative denoising.
- Hyper-network output layer scales with the number of primary network parameters.
- Ground truth epistemic uncertainty cannot be quantified, so EU is validated qualitatively on OOD examples.
Experimental setup
Datasets: LUNA16 ERA5 toy sin(y)+noise dataset
Benchmarks: LUNA16 ERA5 toy inverse problem
Metrics: SSIM PSNR CRPS L1 epistemic/aleatoric uncertainty maps on OOD measurements
Baselines: MC-Dropout DPS-UQ BNN
Builds on: Bayesian hyper-networks conditional diffusion models deep posterior sampling MC dropout Bayes by Backprop
Closest papers by meaning
- Epistemic Uncertainty Quantification For Pre-Trained Neural Networks (CVPR 2024 · similarity 0.86)
- Uncertainty Quantification with the Empirical Neural Tangent Kernel (NeurIPS 2025 · similarity 0.86)
- One Step Closer to Unbiased Aleatoric Uncertainty Estimation (AAAI 2024 · similarity 0.86)
- Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamics (NeurIPS 2025 · similarity 0.85)
- Rethinking Aleatoric and Epistemic Uncertainty (ICML 2025 · similarity 0.85)
- Adaptive Sampling to Reduce Epistemic Uncertainty Using Prediction Interval-Generation Neural Networks (AAAI 2025 · similarity 0.85)
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