The harnessing of machine learning, especially deep generative models, has
opened up promising avenues in the field of synthetic DNA sequence generation.
Whilst Generative Adversarial Networks (GANs) have gained traction for this
application, they often face issues such as limited sample diversity and mode
collapse. On the other hand, Diffusion Models are a promising new class of
generative models that are not burdened with these problems, enabling them to
reach the state-of-the-art in domains such as image generation. In light of
this, we propose a novel latent diffusion model, DiscDiff, tailored for
discrete DNA sequence generation. By simply embedding discrete DNA sequences
into a continuous latent space using an autoencoder, we are able to leverage
the powerful generative abilities of continuous diffusion models for the
generation of discrete data. Additionally, we introduce Fr\'echet
Reconstruction Distance (FReD) as a new metric to measure the sample quality of
DNA sequence generations. Our DiscDiff model demonstrates an ability to
generate synthetic DNA sequences that align closely with real DNA in terms of
Motif Distribution, Latent Embedding Distribution (FReD), and Chromatin
Profiles. Additionally, we contribute a comprehensive cross-species dataset of
150K unique promoter-gene sequences from 15 species, enriching resources for
future generative modelling in genomics. We will make our code public upon
publication