Related papers: Categorical Flow Matching on Statistical Manifolds
Recent efforts have extended the flow-matching framework to discrete generative modeling. One strand of models directly works with the continuous probabilities instead of discrete tokens, which we colloquially refer to as Continuous-State…
Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths…
Generative modeling over discrete data has recently seen numerous success stories, with applications spanning language modeling, biological sequence design, and graph-structured molecular data. The predominant generative modeling paradigm…
Functional data, i.e., smooth random functions observed over a continuous domain, are increasingly available in areas such as biomedical research, health informatics, and epidemiology. However, effective statistical analysis for functional…
We propose Pullback Flow Matching (PFM), a novel framework for generative modeling on data manifolds. Unlike existing methods that assume or learn restrictive closed-form manifold mappings for training Riemannian Flow Matching (RFM) models,…
Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…
Medical image segmentation plays an important role in accurately identifying and isolating regions of interest within medical images. Generative approaches are particularly effective in modeling the statistical properties of segmentation…
Flow Matching (FM) is a recent generative modelling technique: we aim to learn how to sample from distribution $\mathfrak{X}_1$ by flowing samples from some distribution $\mathfrak{X}_0$ that is easy to sample from. The key trick is that…
Distribution-to-distribution generative models support scientific imaging tasks ranging from modeling cellular perturbation responses to translating medical images across conditions. Trustworthy generation requires reliability, or…
We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…
This paper introduces a novel generative model for discrete distributions based on continuous normalizing flows on the submanifold of factorizing discrete measures. Integration of the flow gradually assigns categories and avoids issues of…
Conditional flow matching (CFM) stands out as an efficient, simulation-free approach for training flow-based generative models, achieving remarkable performance for data generation. However, CFM is insufficient to ensure accuracy in…
Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including…
Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this…
We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently…
We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to…
We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…
Combining discrete and continuous data is an important capability for generative models. We present Discrete Flow Models (DFMs), a new flow-based model of discrete data that provides the missing link in enabling flow-based generative models…
Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal…
We provide a theoretical analysis for end-to-end training Discrete Flow Matching (DFM) generative models. DFM is a promising discrete generative modeling framework that learns the underlying generative dynamics by training a neural network…