arXiv research

Paper proposes a new generative model for discrete distributions using flows on submanifolds.

While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. In this paper, we show that flows can in fact be extended to discrete events---and under a simple change-of-variables formula not requiring log-d…

Unified framework for continuous-state discrete flow matching models.

DFMs enable flow-based models for multimodal discrete and continuous data.

Discrete Flow Maps bypass sequential prediction limits for parallel text generation.

IDF++ improves integer discrete flows for lossless compression.

PixelCNN models can achieve state-of-the-art results on CIFAR-10 with exact likelihood computation.

New method reduces discrete flow transitions, improving perplexity estimation.

Unified error analysis for discrete flow models.

Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete random variables such as text, but directly applying normalizing flows to discret…

Corrected samplers reduce discretization error in discrete flow models without additional computational cost.

We introduce the discrete Einstein metrics as critical points of discrete energy on triangulated 3-manifolds, and study them by discrete curvature flow of second (fourth) order. We also study the convergence of the discrete curvature flow. Discrete curvature flow of second order is an analogue of smooth Ricci flow.

Develops a new method for learning discrete distributions without embedding them in a continuous space.

Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous distributions over continuous latent variables. This makes them poorly suited for m…

In this paper, we introduce a parameterized discrete curvature ($α$-curvature) for piecewise linear metrics on polyhedral surfaces, which is a generalization of the classical discrete curvature. A discrete uniformization theorem is established for the parameterized discrete curvature, which generalizes the discrete uni…

Improved sampling quality with RBM-Flow and D-Flow models.

Study of Ricci flow on discrete surfaces of revolution with constant Gaussian curvature.

Branching Flows generates sequences of varying lengths using binary trees.

Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, con…

Generative model for joint discrete distributions using randomized assignment flows.

A discrete method approximates hyperbolic curvature flow in the plane.

ReDi improves few-step generation for discrete data models.

The paper studies deformation of discrete conformal structures on surfaces using combinatorial curvature flows.

New method learns discrete graph diffusion via free-energy gradient flows.

A new method for categorical variational inference using discrete normalizing flows.

Fractional combinatorial flow improves surface conformal structures.

New invertible transformations improve flow-based generative models.

Exact guidance for discrete data improves posterior sampling efficiency.

We define Discrete Quasi-Einstein metrics (DQE-metrics) as the critical points of discrete total curvature functional on triangulated 3-manifolds. We study DQE-metrics by introducing some combinatorial curvature flows. We prove that these flows produce solutions which converge to discrete quasi-Einstein metrics when th…

Study on deforming discrete conformal structures on surfaces with boundaries.

The paper introduces combinatorial curvature and flow for polyhedral surfaces, proving rigidity and solving the Yamabe problem.

Neural networks' feature geometry evolves like discrete Ricci flow.

The paper establishes a discrete uniformization theorem for surfaces with piecewise hyperbolic metrics.

The paper studies stability of discretized Anosov flows.

DDEQs extend DEQs to discrete measure inputs using Wasserstein gradient flows.

DIF extends NF with stochastic discrete latent variables for better density estimation.

New discrete conformal structures on surfaces with boundary, proving global rigidity and constructing hyperbolic metrics.

Bäcklund transformations for smooth and ``space discrete'' Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear Schrödinger equation (NLSE) of Ablowitz and Ladik, when the curve evolves with the Has…

In this paper, we study the discrete Morse flow for the Ricci flow on football, which is the 2-sphere with removed north and south poles and with the metric $g_0$ of constant scalar curvature, and and for Porous media equation on a bounded regular domain in the plane. We show that with a suitable assumption about $g(0)…

The paper studies the consistency of mean curvature flow via volumetric varifolds.

The paper develops algorithms for finding metrics with prescribed combinatorial curvature on polyhedral surfaces.

EB-GFN models discrete data with amortized MCMC sampling.

Exact discrete mechanics for nonholonomic systems defined.

Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.

Paper improves estimates for discrete Laplace in hyperbolic geometry.

In this paper we investigate flows on discrete curves in $\C^2$, $\CP^1$, and $\C$. A novel interpretation of the one dimensional Toda lattice hierarchy and reductions thereof as flows on discrete curves will be given.

Forward-Euler fails for simulating Wasserstein gradient flows with KL divergence.

Ricci-Filtration enhances retrieval-augmented generation rerankers for query-answer tasks by using discrete Ricci flow on graphs.