Related papers: Proximal Residual Flows for Bayesian Inverse Probl…
Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
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…
Challenges in multi-fidelity modeling relate to accuracy, uncertainty estimation and high-dimensionality. A novel additive structure is introduced in which the highest fidelity solution is written as a sum of the lowest fidelity solution…
Through examples of coordinate and probability transformation between different distributions, the basic principle of normalizing flow is introduced in a simple and concise manner. From the perspective of the distribution of random variable…
Recent work demonstrated that flow-based invertible neural networks are promising tools for solving ambiguous inverse problems. Following up on this, we investigate how ten invertible architectures and related models fare on two intuitive,…
Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…
Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
This review provides an introduction to - and overview of - the current state of the art in neural-network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied…
We propose an approach for improving sequence modeling based on autoregressive normalizing flows. Each autoregressive transform, acting across time, serves as a moving frame of reference, removing temporal correlations, and simplifying the…
Differentiable particle filters provide a flexible mechanism to adaptively train dynamic and measurement models by learning from observed data. However, most existing differentiable particle filters are within the bootstrap particle…
Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing…
Neural posterior estimation (NPE), a simulation-based computational approach for Bayesian inference, has shown great success in approximating complex posterior distributions. Existing NPE methods typically rely on normalizing flows, which…
Normalizing flows are diffeomorphic, typically dimension-preserving, models trained using the likelihood of the model. We use the SurVAE framework to construct dimension reducing surjective flows via a new layer, known as the funnel. We…
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…
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling,…
Learning neural networks using only few available information is an important ongoing research topic with tremendous potential for applications. In this paper, we introduce a powerful regularizer for the variational modeling of inverse…
The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…