Variable-Length Generative Protein Design via Generalized Poisson Flow

The ability to generate variable-length proteins is crucial in protein design, where the optimal length is often unknown and tightly coupled to structural designability. Current state-of-the-art diffusion and flow-based generative models require the protein length to be predetermined before sampling, limiting their flexibility in exploring the feasible protein design space. To bridge this gap, we introduce Generalized Poisson Flow (GPFlow), a novel generative framework that enables variable-length generative modeling by learning the rate function that minimizes the negative log-likelihood of an inhomogeneous generalized Poisson process. We establish theoretical guarantees for recovering the joint multimodal distribution (both continuous and discrete) and for an upper bound on the KL divergence to the generated distribution. We evaluate GPFlow extensively across various protein design tasks, including unconditional structure and sequence generation and conditional motif scaffolding, to validate GPFlow’s effectiveness on both continuous and discrete modalities. Our results demonstrate GPFlow’s superior generative performance and quality, achieving the top designability and distributional fitness on unconditional generation, and ranking first on 10 out of 16 motif scaffolding tasks, with up to a 10-fold improvement in success rates on the most challenging targets.