Visual counterfactual explanations (VCEs) have recently gained immense popularity as a tool for clarifying the decision-making process of image classifiers. This trend is largely motivated by what these explanations promise to deliver -- indicate semantically meaningful factors that change the classifier's decision. However, we argue that current state-of-the-art approaches lack a crucial component -- the region constraint -- whose absence prevents from drawing explicit conclusions, and may even lead to faulty reasoning due to phenomenons like confirmation bias. To address the issue of previous methods, which modify images in a very entangled and widely dispersed manner, we propose region-constrained VCEs (RVCEs), which assume that only a predefined image region can be modified to influence the model's prediction. To effectively sample from this subclass of VCEs, we propose Region-Constrained Counterfactual Schrödinger Bridge (RCSB), an adaptation of a tractable subclass of Schrödinger Bridges to the problem of conditional inpainting, where the conditioning signal originates from the classifier of interest. In addition to setting a new state-of-the-art by a large margin, we extend RCSB to allow for exact counterfactual reasoning, where the predefined region contains only the factor of interest, and incorporating the user to actively interact with the RVCE by predefining the regions manually.

Solving inverse problems—recovering signals from incomplete or noisy measurements—is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main paradigms have formed: unsupervised approaches that adapt pretrained generative models to inverse problems, and supervised bridge methods that train stochastic processes conditioned on paired clean and corrupted data. While the former typically assume knowledge of the measurement model, the latter have largely overlooked this structural information. We introduce System-embedded Diffusion Bridge Models (SDBs), a new class of supervised bridge methods that explicitly embed the known linear measurement system into the coefficients of a matrix-valued SDE. This principled integration yields consistent improvements across diverse linear inverse problems and demonstrates robust generalization under system misspecification between training and deployment, offering a promising solution to real-world applications.

Score-based diffusion models are new and powerful tools for image generation. They are based on a forward stochastic process where an image is degraded with additive white noise and optional input scaling. A neural network can be trained to estimate the time-dependent score function, and used to run the reverse-time stochastic process to generate new samples from the training image distribution. However, one issue is that sampling the reverse process requires many passes of the neural network. In this work we present Fourier Diffusion Models which replace the scalar operations of the forward process with linear shift invariant systems and additive spatially-stationary noise. This allows for a model of continuous probability flow from true images to measurements with a specific modulation transfer function (MTF) and noise power spectrum (NPS). We also derive the reverse process for posterior sampling of high-quality images given blurry noisy measurements. We conducted a computational experiment using the Lung Image Database Consortium dataset of chest CT images and simulated CT measurements with correlated noise and system blur. Our results show that Fourier diffusion models can improve image quality for supervised diffusion posterior sampling relative to existing conditional diffusion models.

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term $K$-RCPS, which allows to $(i)$ provide entrywise calibrated intervals for future samples of any diffusion model, and $(ii)$ control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

Spectral CT has shown promise for high-sensitivity quantitative imaging and material decomposition. This work presents a new device called a spatial-spectral filter (SSF) which consists of a tiled array of filter materials positioned near the x-ray source that is used to modulate the spectral shape of the x-ray beam. The filter is moved to obtain projection data that is sparse in each spectral channel. To process this sparse data, we employ a one-step direct model-based material decomposition (MBMD) to reconstruct basis material density images directly from the SSF CT data. To evaluate different possible SSF designs, we define a new Fisher-information-based predictive image quality metric called separability index which characterizes the ability of a spectral CT system to distinguish between the signals from two or more materials. This spectral CT performance metric can be used to optimize spectral CT system design. We conducted simulation-based design optimization study to find optimized combinations of filter materials, filter thicknesses, filter widths, and source settings. Finally, we present MBMD results using simulated SSF CT measurements from the optimized designs to demonstrate the ability to reconstruct basis material density images and to show the benefits of the optimized designs. Our results indicate that optimizing SSF CT for separability leads to high-performance at material discrimination tasks.