Resolving Blind Inverse Problems under Dynamic Range Compression via Structured Forward Operator Modeling

Single-image HDR reconstruction requires inferring missing detail while preserving the visible content of an LDR image. Differences in sensor dynamic range and exposure cause LDR images to lose varying amounts of information in shadows and highlights. We present ExpandDiff, a conditional diffusion pipeline that jointly reconstructs clipped shadows and highlights. To account for this variation, we introduce Dynamic Clipping Synthesis (DCS), which randomly samples shadow and highlight clipping percentiles when constructing training inputs from HDR targets. A pixel-space diffusion model guided by spatially-adaptive normalization then predicts perceptually encoded HDR through a bounded output head, reconstructing both clipping directions in one sampling trajectory. On the SI-HDR benchmark, ExpandDiff variants improve HDR reconstruction accuracy by 3.43 dB in PU21-PSNR over the strongest evaluated competing method, and by 7.34 dB under two-sided clipping. The code and supplementary material are available at https://memreandiran.github.io/expanddiff/.

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely on likelihood approximations that introduce sampling biases. We address these challenges by introducing a new energy-based model trained for denoising with a covariance-based regularization term that enforces consistency across different measurement conditions. The trained model can compute normalized posterior densities for diverse linear inverse problems, without additional retraining or fine tuning. In addition to preserving the sampling capabilities of diffusion models, this enables previously unavailable capabilities: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased Metropolis-Hastings correction steps, and blind estimation of the degradation operator via Bayes rule. We validate the method on multiple datasets (ImageNet, CelebA, AFHQ) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.

Diffusion models are powerful priors for linear inverse problems, but the reference guidance methods, Diffusion Posterior Sampling (DPS) and Pseudoinverse-Guided Diffusion Models ($Π$GDM), rely on scalar hyperparameters tuned per task, usually against the ground truth. We introduce FB-GDM, a fully-Bayesian guided diffusion method that removes this calibration step. Starting from the Gaussian approximation of $Π$GDM, we derive a closed-form conditional score that depends on two precision parameters (inverse variances), one associated with the denoising approximation and one with the observation likelihood, and treat them as latent variables inferred by variational inference at each reverse step. A separable factorization makes each update scale linearly with the number of pixels, so the inference stays tractable at full image resolution, at a cost comparable to one $Π$GDM run. FB-GDM requires neither the noise level nor the ground truth: its only inputs are the observation and the forward operator. Experiments on CelebA-HQ inverse problems establish two results. (i) The precision parameters, inferred from the observation alone, allow FB-GDM to outperform $Π$GDM at its nominal setting, even when the latter is given the true noise level, by up to 14 dB depending on the operator, and to match the ground-truth-calibrated $Π$GDM oracle within 0.1 dB. (ii) FB-GDM is robust when the forward operator, the noise level, or the image distribution changes: it stays close to a per-problem $Π$GDM oracle throughout and does not exhibit the hallucinations observed with DPS, whereas DPS substantially degrades at a fixed scale and $Π$GDM stays competitive only if it is re-tuned against the ground truth for each new problem. When the prior is applied to images outside its training set, this re-balancing between data and prior keeps FB-GDM faithful where a fixed face-prior guidance can otherwise hallucinate.