Measurement Geometry and Design for Trustworthy Generative Inverse Problems

Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions. This distinction is especially important in medical imaging, where acquisition operators are designed under scan-time, dose, and calibration constraints. We study generative inverse problems from a measurement-geometry perspective. The central question is whether a fixed measurement operator can distinguish nearby images that are plausible under the generative prior, and whether this relationship can guide better measurements. We introduce a local measurement-manifold compatibility measure that quantifies how well the operator observes prior-relevant tangent directions. Under local regularity assumptions, we prove that this quantity controls the stable part of the reconstruction error, while the generative prior controls off-manifold drift. This worst-direction certificate motivates practical fixed and sequential acquisition rules based on overall local volume preservation, including a posterior-cloud design that adapts measurements at test time without training a sampling policy. Across row-sampling, tomographic, and MR acquisition settings, the proposed scores predict failure modes, explain measurement-induced hallucinations, and guide better sampling. In fastMRI Cartesian sampling, posterior-cloud measurement design improves over strong non-learned ACS-preserving baselines, including variable-density and Poisson-like masks.

Hallucination-Aware Diffusion Sampling for Inverse Problems via Robust Prior Updates

Diffusion-based inverse problem solvers can produce realistic reconstructions, but realism alone does not ensure that the recovered details are supported by the measurement. We study this failure as measurement-conditioned hallucination: visually meaningful content that is either implausible or inconsistent with the measured instance. Our analysis separates Bayes-rule-based diffusion inverse solvers into a prior update and a measurement-conditioning step, showing that hallucinated content can enter through the prior-side proposal before the measurement correction is applied. Motivated by this view, we propose Robust Prior Update (RPU), a solver-level module that probes the local stability of the diffusion prior update, re-anchors the resulting displacement at the current iterate, and leaves the measurement update unchanged. We instantiate RPU in DPS and evaluate it on FFHQ and ImageNet inverse problems using automatic metrics and human faithfulness studies. On FFHQ, RPU improves PSNR and LPIPS over DPS across box inpainting, Gaussian deblurring, and motion deblurring. In human judgments, RPU receives 91.9% of blind non-tie majority preferences and 91.1% of ground-truth-assisted non-tie preferences on FFHQ box inpainting, while the ImageNet Gaussian reader study is tie-heavy but favors RPU among non-tie cases. These results support a targeted claim: robustifying the prior update can improve instance faithfulness in diffusion inverse solvers, especially when the prior shapes weakly constrained content.

LiFT: Lifted Inter-slice Feature Trajectories for 3D Image Generation from 2D Generators

High-resolution 3D medical image generation remains challenging because fully volumetric models are computationally expensive, while efficient 2D slice generators often fail to preserve anatomical consistency across the third dimension. We propose LiFT, a framework for Lifted inter-slice Feature Trajectories that factorizes 3D volume synthesis into per-slice image generation and inter-slice trajectory learning. Rather than modeling the volumetric distribution end-to-end, LiFT treats a volume as an ordered trajectory in feature space, capturing how anatomical structures appear, transform, and disappear across depth. A tri-planar drifting loss aligns the trajectory of generated slices with the trajectories of real volumes, enabling distributional learning over inter-slice progressions in unconditional generation; in paired translation, a bidirectional $z$-context mixer trained against the registered target supplies through-plane coherence while preserving per-slice fidelity. We evaluate LiFT on BraTS 2023 (unconditional and missing-modality MR) and SynthRAD2023 (MR-to-CT). Across these settings, LiFT preserves per-slice quality, approaches the reported cWDM missing-MR reconstruction quality at $\sim$$135\times$ lower inference cost (without formal equivalence testing), and improves through-plane coherence on MR-to-CT relative to a no-mapper ablation, demonstrating that lightweight inter-slice trajectory learning is a viable route to high-resolution 3D medical synthesis.

DuetFair: Coupling Inter- and Intra-Subgroup Robustness for Fair Medical Image Segmentation

Medical image segmentation models can perform unevenly across subgroups. Most existing fairness methods focus on improving average subgroup performance, implicitly treating each subgroup as internally homogeneous. However, this can hide difficult cases within a subgroup, where high-loss samples are obscured by the subgroup mean. We call this problem \textbf{intra-group hidden failure}. To solve this, we propose \textbf{DuetFair} mechanism, a dual-axis fairness framework that jointly considers inter-subgroup adaptation and intra-subgroup robustness. Based on DuetFair, we introduce \textbf{FairDRO}, which combines distribution-aware mixture-of-experts (dMoE) with subgroup-conditioned distributionally robust optimization (DRO) loss aggregation. This design allows the model to adapt across subgroups while also reducing hidden failures within each subgroup. We evaluate FairDRO on three medical image segmentation benchmarks with varying degrees of within-group heterogeneity. FairDRO achieves the best equity-scaled performance on Harvard-FairSeg and improves worst-case subgroup performance on HAM10000 under both age- and race-based grouping schemes. On the 3D radiotherapy target cohort, FairDRO further improves worst-group Dice by 3.5 points ($\uparrow 6.0\%$) under the tumor-stage grouping and by 4.1 points ($\uparrow 7.4\%$) under the institution grouping over the strongest baseline.

Local Intrinsic Dimension Unveils Hallucinations in Diffusion Models

Diffusion models are prone to generating structural hallucinations - samples that match the statistical properties of the training data yet defy underlying structural rules, resulting in anomalies like hands with more than five fingers. Recent research studied this failure mode from several viewpoints, offering partial explanations to their occurrence, such as mode interpolation. In this work, we propose a complementary perspective that treats hallucinations as instabilities on the model-induced manifold. We begin by showing that a hallucination filter based on such instabilities matches or exceeds the performance of the recently proposed temporal one. By tracing the source of these instabilities, we identify local intrinsic dimension (LID) as their primary driver and propose Intrinsic Quenching (IQ), a direct corrective mechanism that deflates it to alleviate hallucinations. IQ consistently outperforms standard hallucination reduction baselines across a wide array of benchmarks and offers a highly promising solution for enforcing anatomical consistency in downstream medical imaging tasks.

Projection Embedded Diffusion Bridge for CT Reconstruction from Incomplete Data

Reconstructing CT images from incomplete projection data remains challenging due to the ill-posed nature of the problem. Diffusion bridge models have recently shown promise in restoring clean images from their corresponding Filtered Back Projection (FBP) reconstructions, but incorporating data consistency into these models remains largely underexplored. Incorporating data consistency can improve reconstruction fidelity by aligning the reconstructed image with the observed projection data, and can enhance detail recovery by integrating structural information contained in the projections. In this work, we propose the Projection Embedded Diffusion Bridge (PEDB). PEDB introduces a novel reverse stochastic differential equation (SDE) to sample from the distribution of clean images conditioned on both the FBP reconstruction and the incomplete projection data. By explicitly conditioning on the projection data in sampling the clean images, PEDB naturally incorporates data consistency. We embed the projection data into the score function of the reverse SDE. Under certain assumptions, we derive a tractable expression for the posterior score. In addition, we introduce a free parameter to control the level of stochasticity in the reverse process. We also design a discretization scheme for the reverse SDE to mitigate discretization error. Extensive experiments demonstrate that PEDB achieves strong performance in CT reconstruction from three types of incomplete data, including sparse-view, limited-angle, and truncated projections. For each of these types, PEDB outperforms evaluated state-of-the-art diffusion bridge models across standard, noisy, and domain-shift evaluations.

RODS: Robust Optimization Inspired Diffusion Sampling for Detecting and Reducing Hallucination in Generative Models

Diffusion models have achieved state-of-the-art performance in generative modeling, yet their sampling procedures remain vulnerable to hallucinations, often stemming from inaccuracies in score approximation. In this work, we reinterpret diffusion sampling through the lens of optimization and introduce RODS (Robust Optimization-inspired Diffusion Sampler), a novel method that detects and corrects high-risk sampling steps using geometric cues from the loss landscape. RODS enforces smoother sampling trajectories and adaptively adjusts perturbations, reducing hallucinations without retraining and at minimal additional inference cost. Experiments on AFHQv2, FFHQ, and 11k-hands demonstrate that RODS improves both sampling fidelity and robustness, detecting over 70% of hallucinated samples and correcting more than 25%, all while avoiding the introduction of new artifacts.

Surf2CT: Cascaded 3D Flow Matching Models for Torso 3D CT Synthesis from Skin Surface

We present Surf2CT, a novel cascaded flow matching framework that synthesizes full 3D computed tomography (CT) volumes of the human torso from external surface scans and simple demographic data (age, sex, height, weight). This is the first approach capable of generating realistic volumetric internal anatomy images solely based on external body shape and demographics, without any internal imaging. Surf2CT proceeds through three sequential stages: (1) Surface Completion, reconstructing a complete signed distance function (SDF) from partial torso scans using conditional 3D flow matching; (2) Coarse CT Synthesis, generating a low-resolution CT volume from the completed SDF and demographic information; and (3) CT Super-Resolution, refining the coarse volume into a high-resolution CT via a patch-wise conditional flow model. Each stage utilizes a 3D-adapted EDM2 backbone trained via flow matching. We trained our model on a combined dataset of 3,198 torso CT scans (approximately 1.13 million axial slices) sourced from Massachusetts General Hospital (MGH) and the AutoPET challenge. Evaluation on 700 paired torso surface-CT cases demonstrated strong anatomical fidelity: organ volumes exhibited small mean percentage differences (range from -11.1% to 4.4%), and muscle/fat body composition metrics matched ground truth with strong correlation (range from 0.67 to 0.96). Lung localization had minimal bias (mean difference -2.5 mm), and surface completion significantly improved metrics (Chamfer distance: from 521.8 mm to 2.7 mm; Intersection-over-Union: from 0.87 to 0.98). Surf2CT establishes a new paradigm for non-invasive internal anatomical imaging using only external data, opening opportunities for home-based healthcare, preventive medicine, and personalized clinical assessments without the risks associated with conventional imaging techniques.

Cascaded 3D Diffusion Models for Whole-body 3D 18-F FDG PET/CT synthesis from Demographics

We propose a cascaded 3D diffusion model framework to synthesize high-fidelity 3D PET/CT volumes directly from demographic variables, addressing the growing need for realistic digital twins in oncologic imaging, virtual trials, and AI-driven data augmentation. Unlike deterministic phantoms, which rely on predefined anatomical and metabolic templates, our method employs a two-stage generative process. An initial score-based diffusion model synthesizes low-resolution PET/CT volumes from demographic variables alone, providing global anatomical structures and approximate metabolic activity. This is followed by a super-resolution residual diffusion model that refines spatial resolution. Our framework was trained on 18-F FDG PET/CT scans from the AutoPET dataset and evaluated using organ-wise volume and standardized uptake value (SUV) distributions, comparing synthetic and real data between demographic subgroups. The organ-wise comparison demonstrated strong concordance between synthetic and real images. In particular, most deviations in metabolic uptake values remained within 3-5% of the ground truth in subgroup analysis. These findings highlight the potential of cascaded 3D diffusion models to generate anatomically and metabolically accurate PET/CT images, offering a robust alternative to traditional phantoms and enabling scalable, population-informed synthetic imaging for clinical and research applications.

OWT: A Foundational Organ-Wise Tokenization Framework for Medical Imaging

Recent advances in representation learning often rely on holistic, black-box embeddings that entangle multiple semantic components, limiting interpretability and generalization. These issues are especially critical in medical imaging. To address these limitations, we propose an Organ-Wise Tokenization (OWT) framework with a Token Group-based Reconstruction (TGR) training paradigm. Unlike conventional approaches that produce holistic features, OWT explicitly disentangles an image into separable token groups, each corresponding to a distinct organ or semantic entity. Our design ensures each token group encapsulates organ-specific information, boosting interpretability, generalization, and efficiency while allowing fine-grained control in downstream tasks. Experiments on CT and MRI datasets demonstrate the effectiveness of OWT in not only achieving strong image reconstruction and segmentation performance, but also enabling novel semantic-level generation and retrieval applications that are out of reach for standard holistic embedding methods. These findings underscore the potential of OWT as a foundational framework for semantically disentangled representation learning, offering broad scalability and applicability to real-world medical imaging scenarios and beyond.