Learning stochastic cellular dynamics from snapshots through bidirectional causal neural stochastic differential...

Due to cell destruction in sequencing, time-series data yield unpaired snapshots, obscuring lineages and gene dynamics in individual cells. Current data-driven methods rely on single-variate expression, ignoring cell types and rotational effects in nonsteady states, limiting interpretability and accuracy. Each cell's fate diverges to different endpoints and can also flow backward to the starting point. In summary, we propose a bidirectional causal neural network of stochastic differential equation. It jointly trains the forward and reverse processes of the diffusion model to ensure reversible consistency between them, enhancing the stability of the learning process. In the forward process, it models cell differentiation as a stochastic process, whereby the drift term of the stochastic differential equation is learned by discovering causal relationships between principal components. Through multivariate dynamic modeling of unstructured data, the model has better expressiveness and interpretability. Then, we introduce the consistency of cell-type distribution between the predictions and the real data. In the reverse process, we account for the influence of the rotational term on the stochastic differential equation under nonstationary conditions. Instead of simply defining the drift term as the negative gradient of a potential function, we learn it through reverse modeling, thereby constructing an interpretable Waddington potential landscape.