Related papers: Mixed Variational Flows for Discrete Variables
Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively…
Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our…
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…
Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation. Variational approximation is useful when exact inference is intractable or very costly. Our…
Continuously-indexed flows (CIFs) have recently achieved improvements over baseline normalizing flows on a variety of density estimation tasks. CIFs do not possess a closed-form marginal density, and so, unlike standard flows, cannot be…
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…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…
We propose continuous adversarial flow models, a type of continuous-time flow model trained with an adversarial objective. Unlike flow matching, which uses a fixed mean-squared-error criterion, our approach introduces a learned…
Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…
Efficient sampling of complex data distributions can be achieved using trained invertible flows (IF), where the model distribution is generated by pushing a simple base distribution through multiple non-linear bijective transformations.…
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…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
Diffusion models achieve strong generative performance but often rely on large datasets that may include sensitive content. This challenge is compounded by the models' tendency to memorize training data, raising privacy concerns. SFBD (Lu…
Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One…
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…
While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…
Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and…