Variable-Length Generative Protein Design via Generalized Poisson Flow

2026-07-09

AI Summary

Existing protein generative models typically require predefined sequence lengths, limiting design flexibility. This work proposes the Generalized Poisson Flow (GPFlow) framework, which introduces a non-homogeneous generalized Poisson process into protein generation for the first time. By learning the associated rate function, GPFlow enables joint modeling of sequences and structures without requiring fixed-length inputs. The method unifies Euclidean, categorical, and Riemannian geometric modalities, supporting unconditional design, motif scaffolding, and peptide co-design tasks, with theoretical guarantees for target distribution recovery. Experiments demonstrate that GPFlow accurately reproduces natural length distributions, achieves state-of-the-art performance in 10 out of 16 motif scaffolding tasks, and shows competitive results in peptide co-design, significantly outperforming fixed-length baselines.

Abstract

The ability to generate variable-length proteins is crucial in protein design, where the optimal length is often unknown and tightly coupled to designability. Current diffusion- and flow-based generative models typically require the protein length to be specified before sampling, limiting their flexibility in exploring the feasible design space. To address this limitation, we introduce Generalized Poisson Flow (GPFlow), a variable-length generative framework that learns the rate function of an inhomogeneous generalized Poisson process by minimizing its negative log-likelihood. We establish population-level guarantees for recovering the joint multimodal distribution and derive an upper bound on the KL divergence between the data and generated distributions. We comprehensively evaluate GPFlow across structure and sequence design, motif scaffolding, and peptide co-design, spanning Euclidean, categorical, and Riemannian modalities to fully validate its variable-length generation quality. In unconditional design, GPFlow improves structural designability and achieves the best distributional fitness for sequence design compared to their corresponding fixed-length baselines, while perfectly recovering the length distribution. In conditional motif scaffolding, GPFlow ranks first on 10 of 16 structure-based design tasks with significantly more unique successes and also achieves more passed tasks in sequence-based design. In peptide co-design, GPFlow remains competitive even without access to a native-length oracle.

Problem

• variable-length protein design
• generative modeling
• protein length flexibility
• designability
• conditional generation

Innovation

• Generalized Poisson Flow
• variable-length protein generation
• inhomogeneous Poisson process
• multimodal generative modeling
• protein design