LPDP: Inference-Time Reward Control for Variable-Length DNA Generation with Edit Flows

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.

Antibody lead optimization calls for a small, bounded set of edits to an existing candidate: substitutions, but also insertions and deletions. Edit-based generative models are the only ones that allocate such an edit budget without fixing the edit positions, the edit count, or the output length in advance. However, the existing approaches Edit Flows and EvoFlows did not release code or complete training specifications. Here, we show that both methods follow the same underlying process -- edits firing one at a time, at learned rates, in continuous time -- the pure-jump case of generator matching over finite sequences. With EditJumps we introduce the first open implementation of this framework, with a single generalist antibody editor trained on 1.66M Observed Antibody Space homolog pairs to propose homolog-like variants of a seed sequence, editing unseen leads zero-shot, without the per-family retraining original approaches require. Replicating this system from scratch exposes why open code is essential for generative biology: reconciling published edit distributions required reverse-engineering an undocumented rate-scaling hyperparameter that dictates realized mutation counts. Moreover, we show that published evaluation metrics are highly sensitive to reference sample size, frequently flipping method rankings. We release our full codebase, automated test suite, and configurations at: https://github.com/VisiumCH/editjumps

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.