Branching Flows - Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions

Explore a novel generative modeling framework that extends diffusion and flow matching approaches to handle variable-length sequences through stochastic branching and deletion processes. Learn how Branching Flows addresses the fundamental limitation of existing methods that require fixed-size state spaces by allowing elements to evolve over binary tree structures with learnable branching and death rates. Discover how this framework enables models to dynamically control sequence length during generation while maintaining compatibility with flow matching processes across discrete sets, continuous Euclidean spaces, and smooth manifolds. Examine practical applications through three key domains: small molecule generation using multimodal approaches, antibody sequence generation in discrete spaces, and protein backbone generation combining multiple modalities. Understand the theoretical foundations of how Branching Flows transport simple distributions to complex data distributions while providing stable learning objectives and enabling new generative capabilities for AI-driven drug discovery applications.