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QUTCC: Quantile Uncertainty Training and Conformal Calibration for Imaging Inverse Problems

NeurIPS 2026 · Learning theory and algorithms › Prediction and decision losses · approach: Probabilistic calibration · 0 citations (OpenAlex)

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Proposes QUTCC, a quantile-conditioned attention U-Net trained with simultaneous quantile regression whose quantile inputs are calibrated via RCPS to give spatially-adaptive, pixel-wise conformal uncertainty intervals and conditional PDFs for imaging inverse problems.

Problem

Conformal uncertainty intervals for high-dimensional image-to-image inverse problems are loose because calibration uses a single global or fixed-partition scalar and ignores spatial structure, and existing methods cannot produce conditional distributions.

Approach

Train one U-Net conditioned on a continuous quantile embedding with pinball loss over random q, then calibrate the lower and upper quantile inputs (instead of a scalar multiplier) via RCPS-style binary search, yielding non-linear, spatially-adaptive intervals; the same network is queried at multiple quantiles to estimate pixel-wise PDFs.

Key results

• QUTCC achieves the smallest mean interval length among conformal methods on all five tasks (e.g., MRI 0.1083 vs 0.1084 K-RCPS and 0.1096 Im2Im-Deep; Poisson 0.040 vs 0.047 K-RCPS).
• On Poisson denoising in the 0.80–1.00 intensity bin, QUTCC gives 0.187 interval length vs 0.225 for K-RCPS and 0.302 for Im2Im.
• MC-Dropout incurs a 28x–47x inference time increase relative to QUTCC, while Deep Ensembles need roughly 10x more training time; QUTCC is competitive with these posterior baselines on interval length.

Surprising findings

• On real-noise denoising, K-RCPS yields a shorter interval in the high-intensity bin (0.197) than QUTCC (0.286), and Deep Ensembles often yield shorter intervals than QUTCC in several tasks.

Limitations

• Requires paired data for both training and calibration.
• Only pixel-wise marginal coverage guarantees, not joint or spatially structured guarantees.
• Calibration via binary search assumes monotonic learned quantile function; rare quantile crossings occur, mainly in background regions.

Experimental setup

Datasets: Gaussian denoising data Poisson denoising data real-noise microscopy denoising data accelerated MRI data quantitative phase imaging data

Benchmarks: accelerated MRI quantitative phase imaging Gaussian denoising Poisson denoising real-noise denoising

Metrics: mean interval length total miscoverage risk MSE SSIM PSNR LPIPS inference time

Baselines: MC-Dropout Deep Ensembles Im2Im Im2Im-Asymm K-RCPS

Builds on: Im2Im-UQ RCPS K-RCPS deep ensembles MC-Dropout

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