Correlated latent space learning for structural differentiation modeling in single cell RNA data

Single-cell RNA sequencing (scRNA-seq) enables high-resolution analysis of cellular differentiation, yet many existing methods have difficulty modeling its continuous, coupled, and noise-prone dynamics. We present CODEVAE (Correlated Ordinary Differential Equation Variational Autoencoder), a deep generative framework that integrates ordinary differential equation constraints with correlation-aware latent representations to preserve geometric continuity and biologically coupled variation. Building on a baseline variational autoencoder, CODEVAE incrementally incorporates low-$\beta$ regularization, an information bottleneck reconstruction pathway, ODE-based continuity, and correlated latent components. Across an evaluation suite of 18 metrics and 55 independent runs, CODEVAE achieves consistently higher performance than advanced variational models, single-cell specific methods, graph/contrastive approaches, and traditional dimensionality reduction techniques. In multi-batch settings, CODEVAE maintains smooth manifolds and attains improved integration quality. In biological applications, CODEVAE reconstructs a continuous megakaryocyte differentiation trajectory and delineates stage-specific effects of Dapp1 perturbation. These findings position CODEVAE as a robust, principled approach for modeling continuous cellular dynamics and extracting mechanistic insights across diverse single-cell contexts.