  This paper introduces a novel framework for DNA sequence generation,
comprising two key components: DiscDiff, a Latent Diffusion Model (LDM)
tailored for generating discrete DNA sequences, and Absorb-Escape, a
post-training algorithm designed to refine these sequences. Absorb-Escape
enhances the realism of the generated sequences by correcting `round errors'
inherent in the conversion process between latent and input spaces. Our
approach not only sets new standards in DNA sequence generation but also
demonstrates superior performance over existing diffusion models, in generating
both short and long DNA sequences. Additionally, we introduce EPD-GenDNA, the
first comprehensive, multi-species dataset for DNA generation, encompassing
160,000 unique sequences from 15 species. We hope this study will advance the
generative modelling of DNA, with potential implications for gene therapy and
protein production.
