Related papers: Generative Unfolding with Distribution Mapping

We propose to learn a generative model via entropy interpolation with a Schr\"{o}dinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the…

Flow-based generative models have demonstrated promising performance across a broad spectrum of data modalities (e.g., image and text). However, there are few works exploring their extension to unordered data (e.g., spatial point set),…

Diffusion models often yield highly curved trajectories and noisy score targets due to an uninformative, memoryless forward process that induces independent data-noise coupling. We propose Adjoint Schr\"odinger Bridge Matching (ASBM), a…

Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these…

Direct prediction of material properties from microstructures through statistical models has shown to be a potential approach to accelerating computational material design with large design spaces. However, statistical modeling of highly…

We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…

High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing…

We formulate the inverse problem in a Bayesian framework and aim to train a generative model that allows us to simulate (i.e., sample from the likelihood) and do inference (i.e., sample from the posterior). We review the use of triangular…

Denoising diffusion models are a novel class of generative models that have recently become extremely popular in machine learning. In this paper, we describe how such ideas can also be used to sample from posterior distributions and, more…

In this paper we describe a novel framework for diffusion-based generative modeling on constrained spaces. In particular, we introduce manual bridges, a framework that expands the kinds of constraints that can be practically used to form…

Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer…

Likelihood-based, or explicit, deep generative models use neural networks to construct flexible high-dimensional densities. This formulation directly contradicts the manifold hypothesis, which states that observed data lies on a…

We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields,…

Optimising probabilistic models is a well-studied field in statistics. However, its connection with the training of generative models remains largely under-explored. In this paper, we show that the evolution of time-varying generative…

Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using a large number of samples. When trained successfully, we can use the DGMs to…

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…

Deep generative models learn the data distribution, which is concentrated on a low-dimensional manifold. The geometric analysis of distribution transformation provides a better understanding of data structure and enables a variety of…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

Diffusion Probabilistic Methods are employed for state-of-the-art image generation. In this work, we present a method for extending such models for performing image segmentation. The method learns end-to-end, without relying on a…