Transport-Based and Flow Map Learning Generative Models: Advances and Perspectives

Dear Colleagues,

In recent years, the breakthrough of generative models‘ performance on disparate applications has raised a huge interest in real-world challenges. In particular, the evolution of Deep Generative Models (DGMs) is crucial since they are deep learning algorithms designed for characterizing and sampling high-dimensional data distributions. By capturing the underlying probability distribution generating training samples, it can synthesize new realistic data-solving and, hence, complex tasks, such as image restoration and super-resolution, and improve autonomous decision-making systems.

In DGMs, the most promising approaches are (1) transport-based and (2) flow map learning generative, justifying the particular attention paid in this Special Issue towards them.

Transport-based generative modeling is a mathematical framework that offers a rigorous convergence of the algorithms, guaranteeing that the probability distribution generated is quite close to the underlying one of training samples. This framework is characterized by replacing traditional adversarial or variational approaches with a rigorous theoretical foundation based on optimal transport, diffusion models, flow matching, and bridge processes. Such models provide a unified mathematical framework that ensures more stable training and superior performance in both generative and prediction (i.e., classification and regression) tasks.

However, transport-based frameworks typically rely on the numerical solution of a differential equation for sample generation, requiring an iterated evaluation of the learned model. This limitation has fostered the development of accelerated inference techniques. Promising developments in flow map learning, such as consistency models, have emerged to address this by directly estimating the flow map associated with the probability flow equation, rather than the velocity fields governing its instantaneous dynamics. Removing the need for iterative evaluations, these flow map approaches can reduce inference time by two orders of magnitude compared with traditional transport-based models, opening new horizons in generative artificial intelligence.

This Special Issue aims to collect high-quality research articles on transport-based and flow-map learning methods for solving complex generative and real-world problems. The goal of this Special Issue is to promote the improvement of the accuracy and efficiency of existing generative approaches. This Special Issue will pay particular attention to real-world applications of transport-based and flow-map learning methodologies, without excluding any specific domains.

Dr. Thierry Bouwmans
Dr. Emanuel Di Nardo
Dr. Chieh-Hsin Lai
Dr. Francesco Camastra
Guest Editors

Angelo Casolaro, PhD student
Guest Editor Assistant
Email: angelo.casolaro001@studenti.uniparthenope.it
Affiliation: CVPRLab “Alfredo Petrosino”, University of Naples Parthenope, 80133 Naples, Italy
Website: https://www.linkedin.com/in/angelo-casolaro/
Interest: deep generative models; spatio-temporal series prediction; bayesian models

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• transport-based generative models
• flow map learning
• deep generative models
• consistency models
• diffusion models
• flow matching models
• stochastic interpolants
• generative AI for science