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Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) based on explicit Euler steps of negative gradient flows and…
Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is…
We show that any open set that is a finite distance away from a Lipschitz subgraph will become a Lipschitz subgraph after flowing under fractional mean curvature flow for a finite, universal time. Our proof is quantitative and inherently…
Normalizing flows are a class of deep generative models that provide a promising route to sample lattice field theories more efficiently than conventional Monte Carlo simulations. In this work we show that the theoretical framework of…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
Flow-matching models provide a powerful framework for various applications, offering efficient sampling and flexible probability path modeling. These models are characterized by flows with low curvature in learned generative trajectories,…
Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model…
Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a…
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…
We consider the problem of approximating flow functions of continuous-time dynamical systems with inputs. It is well-known that continuous-time recurrent neural networks are universal approximators of this type of system. In this paper, we…
Generative modeling seeks to uncover the underlying factors that give rise to observed data that can often be modeled as the natural symmetries that manifest themselves through invariances and equivariances to certain transformation laws.…
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…
Systems biology relies on mathematical models that often involve complex and intractable likelihood functions, posing challenges for efficient inference and model selection. Generative models, such as normalizing flows, have shown…
Continuous normalizing flows (CNFs) are a generative method for learning probability distributions, which is based on ordinary differential equations. This method has shown remarkable empirical success across various applications, including…
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…
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…
We present a novel theoretical framework for understanding the expressive power of normalizing flows. Despite their prevalence in scientific applications, a comprehensive understanding of flows remains elusive due to their restricted…
Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz constant. However, approximation-theoretic guarantees for…
Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the…