Probing the Geometry of Data with Diffusion Fréchet Functions
Many complex ecosystems, such as those formed by multiple microbial taxa, involve intricate interactions amongst various sub-communities. The most basic relationships are frequently modeled as co-occurrence networks in which the nodes represent the various players in the community and the weighted edges encode levels of interaction. In this setting, the composition of a community may be viewed as a probability distribution on the nodes of the network. This paper develops methods for modeling the organization of such data, as well as their Euclidean counterparts, across spatial scales. Using the notion of diffusion distance, we introduce diffusion Frechet functions and diffusion Frechet vectors associated with probability distributions on Euclidean space and the vertex set of a weighted network, respectively. We prove that these functional statistics are stable with respect to the Wasserstein distance between probability measures, thus yielding robust descriptors of their shapes. We apply the methodology to investigate bacterial communities in the human gut, seeking to characterize divergence from intestinal homeostasis in patients with Clostridium difficile infection (CDI) and the effects of fecal microbiota transplantation, a treatment used in CDI patients that has proven to be significantly more effective than traditional treatment with antibiotics. The proposed method proves useful in deriving a biomarker that might help elucidate the mechanisms that drive these processes.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Consistent Mesh Diffusion
Given a 3D mesh with a UV parameterization, we introduce a novel approach to generating textures from text prompts. While prior work uses optimization from Text-to-Image Diffusion models to generate textures and geometry…
AdvFD: Boosting Visual Generation via Adversarial Fr'echet Distance Loss
Fréchet distance has recently emerged as an effective distribution-level objective for generator post-training, complementing the conventional sample-level diffusion and flow-matching losses. However, directly optimizing…
Geometry-Aware Discretization Error of Diffusion Models
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is of…
Image GenerationRiemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions
Classical archetypal analysis is appealing for its interpretability, but its linear geometry can limit performance on data with strongly non-linear structure; at the same time, existing neural extensions improve flexibil…
Diffusion Model Attribution via Spectral Coupling of Denoiser Responses
Attributing a generated image to its source diffusion model is a fundamental challenge in provenance verification and intellectual property protection. This problem is particularly difficult because diffusion models trai…