Related papers: Manifold-Aligned Generative Transport

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…

We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…

We are interested in learning generative models for complex geometries described via manifolds, such as spheres, tori, and other implicit surfaces. Current extensions of existing (Euclidean) generative models are restricted to specific…

Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…

Unsupervised domain mapping has attracted substantial attention in recent years due to the success of models based on the cycle-consistency assumption. These models map between two domains by fooling a probabilistic discriminator, thereby…

Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…

This paper raises an implicit manifold learning perspective in Generative Adversarial Networks (GANs), by studying how the support of the learned distribution, modelled as a submanifold $\mathcal{M}_{\theta}$, perfectly match with…

Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…

We propose a novel modular inference approach combining two different generative models -- generative adversarial networks (GAN) and normalizing flows -- to approximate the posterior distribution of physics-based Bayesian inverse problems…

Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…

The conventional understanding of adversarial training in generative adversarial networks (GANs) is that the discriminator is trained to estimate a divergence, and the generator learns to minimize this divergence. We argue that despite the…

Unpaired image-to-image translation has been applied successfully to natural images but has received very little attention for manifold-valued data such as in diffusion tensor imaging (DTI). The non-Euclidean nature of DTI prevents current…

We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models. MGM is based on a simple symmetry of Flow Matching with linear interpolation: when the two endpoint distributions coincide, the…

Flow matching has emerged as a powerful framework for generative modeling, with recent empirical successes highlighting the effectiveness of signal-space prediction ($x$-prediction). In this work, we investigate the transfer of this…

Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially…

Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…

Current discriminative depth estimation methods often produce blurry artifacts, while generative approaches suffer from slow sampling due to curvatures in the noise-to-depth transport. Our method addresses these challenges by framing depth…

Recent deep generative models are able to provide photo-realistic images as well as visual or textual content embeddings useful to address various tasks of computer vision and natural language processing. Their usefulness is nevertheless…

Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and…

The bifurcation of generative modeling into autoregressive approaches for discrete data (text) and diffusion approaches for continuous data (images) hinders the development of truly unified multimodal systems. While Masked Language Models…