Single-cell Gene Expression Generation with Hybrid Discrete-Continuous Diffusion

Single-cell gene expression data is an important pathway to understanding the fundamentals of various cellular applications, like disease tracking and drug targeting. Obtaining high-quality single-cell data is challenging due to the high cost compared to bulk sequencing. This has led to the use of generative models to create synthetic data. The goal is to efficiently generate realistic cells, as that is vital for stronger downstream analysis for applications like cell trajectories and differentiations. Current directions either use purely continuous or purely discrete diffusion to tackle this challenge. Using a purely continuous method allows the model to learn the joint expression levels through a continuous score function. This lets the model learn any potential cellular connections between each gene expression. Using a discrete method respects the sparse nature of the data, removing any representational mismatch that occurs from working in a continuous to discrete space. We propose to leverage the best of both worlds through $\text{scCANDI}$: single-cell continuous and discrete diffusion. We highlight the differences between continuous and discrete diffusion through a case study, pinpointing the exact differences in the generated cell profiles under discrete, continuous, and hybrid settings. We demonstrate that scCANDI achieves strong performance against current state-of-the-art masked discrete diffusion methods while requiring \textbf{5-10\times} fewer function evaluations.