On conditional Markov bridges

Thursday 4 Jul 2024, 10:00 → 11:00 Europe/Berlin

Zoom Meeting: https://uni-bonn.zoom-x.de/j/66937265800?pwd=ajkn2kuFvMYoUBkhGnaAZOMKidm9JN.1

Speaker: Dr. Cesar Ojeda.

 

Abstract: In this talk I will present a novel generative modeling framework for discrete state spaces using continuous-time Conditional Markov Bridges (CMB). Unlike traditional diffusion models, which often assume a Gaussian target distribution, our method constructs a Markov Jump Process that accurately captures the joint distribution of arbitrary initial and final states. By marginalizing the rate of the conditional Markov bridge over the joint posterior probability, we achieve efficient sampling without iterative Sinkhorn updates. This method extends the principles of flow-based and diffusion-based models to discrete variables, allowing for the introduction of non-trivial transport maps between complex distributions through marginalization. Our experiments demonstrate significant improvements in generating high-quality discrete data across various synthetic and real-world datasets, including binary image generation and graph generation tasks. The proposed CMB framework provides a robust and efficient approach to generative modeling in discrete state spaces, offering stable training objectives and fast inference times.