Flexible Flows for Biological Sequence Design

Abstract: Designing functional biological sequences requires navigating vast discrete spaces under strict evolutionary and biophysical constraints. Discrete Flow Matching (DFM) offers a generative framework over such spaces, but existing approaches rely on biologically uninformative couplings and offer limited flexibility for variable-length sequence generation and fine-grained control. We propose a structured coupling that encodes domain-specific preferences among sequence elements, biasing the source distribution toward plausible regions without modifying the flow objective or training procedure. Building on this, we introduce a latent edit-based rate parameterization that models variable-length generation via edit operations conditioned on a shared global latent, akin to a latent variable model, while remaining tractable. We further introduce a latent classifier-free guidance mechanism that steers generation coherently in continuous latent space, along with Dirichlet-prior temperature scaling for test-time control over edit operations. Our method achieves state-of-the-art performance across diverse biological sequence tasks, including density estimation, unconditional and conditional DNA sequence generation, and peptide sequence generation.