Related papers: Analytic Bijections for Smooth and Interpretable N…

Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios.…

We show that normalising flows become pathological when used to model targets whose supports have complicated topologies. In this scenario, we prove that a flow must become arbitrarily numerically noninvertible in order to approximate the…

Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…

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…

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 have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction. We propose here an in-depth…

Normalizing flows are among the most popular paradigms in generative modeling, especially for images, primarily because we can efficiently evaluate the likelihood of a data point. This is desirable both for evaluating the fit of a model,…

Normalizing flows model complex probability distributions by combining a base distribution with a series of bijective neural networks. State-of-the-art architectures rely on coupling and autoregressive transformations to lift up invertible…

Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of a simple base distribution. However, there are often applications that require more than invertibility. For instance,…

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…

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 deep generative models that allow efficient likelihood calculation and sampling. The core requirement for this advantage is that they are constructed using functions that can be efficiently inverted and for which the…

Normalizing flows are bijective mappings between inputs and latent representations with a fully factorized distribution. They are very attractive due to exact likelihood valuation and efficient sampling. However, their effective capacity is…

Continuous normalizing flows are known to be highly expressive and flexible, which allows for easier incorporation of large symmetries and makes them a powerful computational tool for lattice field theories. Building on previous work, we…

Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow…

Normalising flows offer a flexible way of modelling continuous probability distributions. We consider expressiveness, fast inversion and exact Jacobian determinant as three desirable properties a normalising flow should possess. However,…

Let $\mathbf{x}=(x,y)$. A projective 2-dimensional flow is a solution to a 2-dimensional projective translation equation (PrTE) $(1-z)\phi(\mathbf{x})=\phi(\phi(\mathbf{x}z)(1-z)/z)$, $\phi:\mathbb{C}^{2}\mapsto\mathbb{C}^{2}$. Previously…

Normalizing flows (NFs) provide a powerful tool to construct an expressive distribution by a sequence of trackable transformations of a base distribution and form a probabilistic model of underlying data. Rotation, as an important quantity…

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…

Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced,…