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

arXiv: https://arxiv.org/abs/2605.11368 · HTML: https://mlsanity.com/paper/2605.11368/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 10 of its 27 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 10 of 10)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Beam Search Strategies for Neural Machine Translation](https://mlsanity.com/paper/1702.01806/) (2017)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [Dirichlet Diffusion Score Model for Biological Sequence Generation](https://mlsanity.com/paper/2305.10699/) (2023)
- [Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Design](https://mlsanity.com/paper/2410.13643/) (2024)
- [Edit Flows: Flow Matching with Edit Operations](https://mlsanity.com/paper/2506.09018/) (2025)
- [Reward-Guided Iterative Refinement in Diffusion Models at Test-Time with Applications to Protein and DNA Design](https://mlsanity.com/paper/2502.14944/) (2025)
- [D3LM: A Discrete DNA Diffusion Language Model for Bidirectional DNA Understanding and Generation](https://mlsanity.com/paper/2603.01780/) (2026)

## Abstract (arXiv)

We study the application of recent Edit Flows for inference-time reward control for DNA sequence generation. Unlike most reward-guided DNA generation frameworks, which operate on fixed-length sequence spaces, Edit Flows have a potential to generate variable-length DNA through biologically plausible insertion, deletion, and substitution operations. In particular, we propose Local Perturbation Discrete Programming (LPDP), a training-free, intermediate-state and action-aware local re-solving operator for variable-length DNA edit-action generators at inference time. More specifically, at each guided rollout step, LPDP scores one-step root edits, retains a near-best root band, and re-ranks each retained root by solving a bounded local discrete program around its child sequence. This local program uses the typed geometry of edit actions to focus on coherent substitution, insertion, or deletion subgraphs, and aggregates local continuations with either a hard Max backup or a soft log-sum-exponential (LSE) backup. We instantiate LPDP in two regimes: front-loaded reward tilting for enhancer optimization, where early edits are critical for establishing global regulatory sequence structure, and back-loaded reward tilting for exon-intron-exon inpainting, where late edits fine-tune splice-boundary contexts.