Related papers: Invertible Monotone Operators for Normalizing Flow…
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only…
Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…
A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the…
In this paper, we analyze the properties of invertible neural networks, which provide a way of solving inverse problems. Our main focus lies on investigating and controlling the Lipschitz constants of the corresponding inverse networks.…
An invertible function is bi-Lipschitz if both the function and its inverse have bounded Lipschitz constants. Nowadays, most Normalizing Flows are bi-Lipschitz by design or by training to limit numerical errors (among other things). In this…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…
Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…
Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…
Normalizing flows define a probability distribution by an explicit invertible transformation $\boldsymbol{\mathbf{z}}=f(\boldsymbol{\mathbf{x}})$. In this work, we present implicit normalizing flows (ImpFlows), which generalize normalizing…
A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that…
Normalizing flows are objects used for modeling complicated probability density functions, and have attracted considerable interest in recent years. Many flexible families of normalizing flows have been developed. However, the focus to date…
Normalizing flows, which learn a distribution by transforming the data to samples from a Gaussian base distribution, have proven powerful density approximations. But their expressive power is limited by this choice of the base distribution.…
A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based…
Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…
In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…
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…
The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…
Modeling real-world distributions can often be challenging due to sample data that are subjected to perturbations, e.g., instrumentation errors, or added random noise. Since flow models are typically nonlinear algorithms, they amplify these…
Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise.…