Likely Interpolants of Generative Models

Interpolation in generative models allows for controlled generation, model inspection, and more. Unfortunately, most generative models lack a principal notion of interpolants without restrictive assumptions on either the model or data dimension. In this paper, we develop a general interpolation scheme that targets likely transition paths compatible with different metrics and probability distributions. We consider interpolants analogous to a geodesic constrained to a suitable data distribution and derive a novel algorithm for computing these curves, which requires no additional training. Theoretically, we show that our method locally can be considered as a geodesic under a suitable Riemannian metric. We quantitatively show that our interpolation scheme traverses higher density regions than baselines across a range of models and datasets.

Point-Based Shape Representation Generation with a Correspondence-Preserving Diffusion Model

We propose a diffusion model designed to generate point-based shape representations with correspondences. Traditional statistical shape models have considered point correspondences extensively, but current deep learning methods do not take them into account, focusing on unordered point clouds instead. Current deep generative models for point clouds do not address generating shapes with point correspondences between generated shapes. This work aims to formulate a diffusion model that is capable of generating realistic point-based shape representations, which preserve point correspondences that are present in the training data. Using shape representation data with correspondences derived from Open Access Series of Imaging Studies 3 (OASIS-3), we demonstrate that our correspondence-preserving model effectively generates point-based hippocampal shape representations that are highly realistic compared to existing methods. We further demonstrate the applications of our generative model by downstream tasks, such as conditional generation of healthy and AD subjects and predicting morphological changes of disease progression by counterfactual generation.

MedIL: Implicit Latent Spaces for Generating Heterogeneous Medical Images at Arbitrary Resolutions

In this work, we introduce MedIL, a first-of-its-kind autoencoder built for encoding medical images with heterogeneous sizes and resolutions for image generation. Medical images are often large and heterogeneous, where fine details are of vital clinical importance. Image properties change drastically when considering acquisition equipment, patient demographics, and pathology, making realistic medical image generation challenging. Recent work in latent diffusion models (LDMs) has shown success in generating images resampled to a fixed-size. However, this is a narrow subset of the resolutions native to image acquisition, and resampling discards fine anatomical details. MedIL utilizes implicit neural representations to treat images as continuous signals, where encoding and decoding can be performed at arbitrary resolutions without prior resampling. We quantitatively and qualitatively show how MedIL compresses and preserves clinically-relevant features over large multi-site, multi-resolution datasets of both T1w brain MRIs and lung CTs. We further demonstrate how MedIL can influence the quality of images generated with a diffusion model, and discuss how MedIL can enhance generative models to resemble raw clinical acquisitions.

Quantifying Hippocampal Shape Asymmetry in Alzheimer's Disease Using Optimal Shape Correspondences

Hippocampal atrophy in Alzheimer's disease (AD) is asymmetric and spatially inhomogeneous. While extensive work has been done on volume and shape analysis of atrophy of the hippocampus in AD, less attention has been given to hippocampal asymmetry specifically. Previous studies of hippocampal asymmetry are limited to global volume or shape measures, which don't localize shape asymmetry at the point level. In this paper, we propose to quantify localized shape asymmetry by optimizing point correspondences between left and right hippocampi within a subject, while simultaneously favoring a compact statistical shape model of the entire sample. To account for related variables that have impact on AD and healthy subject differences, we build linear models with other confounding factors. Our results on the OASIS3 dataset demonstrate that compared to using volumetric information, shape asymmetry reveals fine-grained, localized differences that indicate the hippocampal regions of most significant shape asymmetry in AD patients.