Related papers: Semi-Discrete Normalizing Flows through Differenti…
Diffusion models, and their generalization, flow matching, have had a remarkable impact on the field of media generation. Here, the conventional approach is to learn the complex mapping from a simple source distribution of Gaussian noise to…
In this study, we use Rational-Quadratic Neural Spline Flows, a sophisticated parametrization of Normalizing Flows, for inferring posterior probability distributions in scenarios where direct evaluation of the likelihood is challenging at…
We present an novel framework for efficiently and effectively extending the powerful continuous diffusion processes to discrete modeling. Previous approaches have suffered from the discrepancy between discrete data and continuous modeling.…
Computing the Voronoi diagram of mixed geometric objects in $R^3$ is challenging due to the high cost of exact geometric predicates via Cylindrical Algebraic Decomposition (CAD). We propose an efficient exact verification framework that…
Reliable quantification of epistemic and aleatoric uncertainty is of crucial importance in applications where models are trained in one environment but applied to multiple different environments, often seen in real-world applications for…
The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided…
Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation,…
Topology optimization (TO) can be viewed as seeking an optimal solution in the design space of a given TO problem. For weakly non-linear TO problems, e.g., compliance minimization, sensitivity-based methods typically converge well, whereas…
Many problems in fluid dynamics are effectively modeled as Stokes flows - slow, viscous flows where the Reynolds number is small. Boundary integral equations are often used to solve these problems, where the fundamental solutions for the…
Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function…
Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…
An ultimate objective in continual learning is to preserve knowledge learned in preceding tasks while learning new tasks. To mitigate forgetting prior knowledge, we propose a novel knowledge distillation technique that takes into the…
Normalizing flows learn a diffeomorphic mapping between the target and base distribution, while the Jacobian determinant of that mapping forms another real-valued function. In this paper, we show that the Jacobian determinant mapping is…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…
The isolation of pure samples of quark and gluon jets is of key interest at hadron colliders. Recent work has employed topic modeling to disentangle the underlying distributions in mixed samples obtained from experiments. However, current…
Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by…
Coupling-based normalizing flows (e.g. RealNVP) are a popular family of normalizing flow architectures that work surprisingly well in practice. This calls for theoretical understanding. Existing work shows that such flows weakly converge to…
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…
Normalizing flows map an independent set of latent variables to their samples using a bijective transformation. Despite the exact correspondence between samples and latent variables, their high level relationship is not well understood. In…