Single-cell RNA sequencing (scRNA-seq), especially temporally resolved datasets, enables genome-wide profiling of gene expression dynamics at single-cell resolution across discrete time points. However, current technologies provide only sparse, static snapshots of cell states and are inherently influenced by technical noise, complicating the inference and representation of continuous transcriptional dynamics. Although embedding methods can reduce dimensionality and mitigate technical noise, the majority of existing approaches typically treat trajectory inference separately from embedding construction, often neglecting temporal structure. To address this challenge, here we introduce CellStream, a novel deep learning framework that jointly learns embedding and cellular dynamics from single-cell snapshots data by integrating an autoencoder with unbalanced dynamical optimal transport. Compared to existing methods, CellStream generates dynamics-informed embeddings that robustly capture temporal developmental processes while maintaining high consistency with the underlying data manifold. We demonstrate CellStream’s effectiveness on both simulated datasets and real scRNA-seq data, including spatial transcriptomics. Our experiments indicate significant quantitative improvements over state-of-the-art methods in representing cellular trajectories with enhanced temporal coherence and reduced noise sensitivity. Overall, CellStream provides a new tool for learning and representing continuous streams from the noisy, static snapshots of single-cell gene expression.

Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal transport (RUOT) and inferring continuous unbalanced stochastic dynamics from observed snapshots. Based on the RUOT form, our method models these dynamics without requiring prior knowledge of growth and death processes or additional information, allowing them to be learned directly from data. Theoretically, we explore the connections between the RUOT and Schrödinger bridge problem and discuss the key challenges and potential solutions. The effectiveness of our method is demonstrated with a synthetic gene regulatory network, high-dimensional Gaussian Mixture Model, and single-cell RNA-seq data from blood development. Compared with other methods, our approach accurately identifies growth and transition patterns, eliminates false transitions, and constructs the Waddington developmental landscape. Our code is available at: [https://github.com/zhenyiizhang/DeepRUOT](https://github.com/zhenyiizhang/DeepRUOT).

Recovering the dynamics from a few snapshots of a high-dimensional system is a challenging task in statistical physics and machine learning, with important applications in computational biology. Many algorithms have been developed to tackle this problem, based on frameworks such as optimal transport and the Schrödinger bridge. A notable recent framework is Regularized Unbalanced Optimal Transport (RUOT), which integrates both stochastic dynamics and unnormalized distributions. However, since many existing methods do not explicitly enforce optimality conditions, their solutions often struggle to satisfy the principle of least action and meet challenges to converge in a stable and reliable way. To address these issues, we propose Variational RUOT (Var-RUOT), a new framework to solve the RUOT problem. By incorporating the optimal necessary conditions for the RUOT problem into both the parameterization of the search space and the loss function design, Var-RUOT only needs to learn a scalar field to solve the RUOT problem and can search for solutions with lower action. We also examined the challenge of selecting a growth penalty function in the widely used Wasserstein-Fisher-Rao metric and proposed a solution that better aligns with biological priors in Var-RUOT. We validated the effectiveness of Var-RUOT on both simulated data and real single-cell datasets. Compared with existing algorithms, Var-RUOT can find solutions with lower action while exhibiting faster convergence and improved training stability. Our code is available at https://github.com/ZerooVector/VarRUOT.

Learning the underlying dynamics of single cells from snapshot data has gained increasing attention in scientific and machine learning research. The destructive measurement technique and cell proliferation/death result in unpaired and unbalanced data between snapshots, making the learning of the underlying dynamics challenging. In this paper, we propose joint Velocity-Growth Flow Matching (VGFM), a novel paradigm that jointly learns state transition and mass growth of single-cell populations via flow matching. VGFM builds an ideal single-cell dynamics containing velocity of state and growth of mass, driven by a presented two-period dynamic understanding of the static semi-relaxed optimal transport, a mathematical tool that seeks the coupling between unpaired and unbalanced data. To enable practical usage, we approximate the ideal dynamics using neural networks, forming our joint velocity and growth matching framework. A distribution fitting loss is also employed in VGFM to further improve the fitting performance for snapshot data. Extensive experimental results on both synthetic and real datasets demonstrate that VGFM can capture the underlying biological dynamics accounting for mass and state variations over time, outperforming existing approaches for single-cell dynamics modeling.

Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schrödinger bridge theory, or their variants to simultaneously infer stochastic, unbalanced dynamics from snapshot data. However, these approaches remain limited in their ability to account for cell-cell interactions. This integration is essential in real-world scenarios since intercellular communications are fundamental life processes and can influence cell state-transition dynamics. To address this challenge, we formulate the Unbalanced Mean-Field Schrödinger Bridge (UMFSB) framework to model unbalanced stochastic interaction dynamics from snapshot data. Inspired by this framework, we further propose CytoBridge, a deep learning algorithm designed to approximate the UMFSB problem. By explicitly modeling cellular transitions, proliferation, and interactions through neural networks, CytoBridge offers the flexibility to learn these processes directly from data. The effectiveness of our method has been extensively validated using both synthetic gene regulatory data and real scRNA-seq datasets. Compared to existing methods, CytoBridge identifies growth, transition, and interaction patterns, eliminates false transitions, and reconstructs the developmental landscape with greater accuracy. Code is available at: https://github.com/zhenyiizhang/CytoBridge-NeurIPS.

With the rapid development of single-cell sequencing techniques, several large-scale cell atlas projects have been launched across the world. However, it is still challenging to integrate single-cell RNA-seq (scRNA-seq) datasets with diverse tissue sources, developmental stages and/or few overlaps, due to the ambiguity in determining the batch information, which is particularly important for current batch-effect correction methods. Here, we present SCORE, a simple network-based integration methodology, which incorporates curated molecular network features to infer cellular states and generate a unified workflow for integrating scRNA-seq datasets. Validating on real single-cell datasets, we showed that regardless of batch information, SCORE outperforms existing methods in accuracy, robustness, scalability and data integration.

Single-cell RNA sequencing trades read-depth for dimensionality, often leading to loss of critical signaling gene information that is typically present in bulk data sets. We introduce DURIAN (Deconvolution and mUltitask-Regression-based ImputAtioN), an integrative method for recovery of gene expression in single-cell data. Through systematic benchmarking, we demonstrate the accuracy, robustness and empirical convergence of DURIAN using both synthetic and published data sets. We show that use of DURIAN improves single-cell clustering, low-dimensional embedding, and recovery of intercellular signaling networks. Our study resolves several inconsistent results of cell-cell communication analysis using single-cell or bulk data independently. The method has broad application in biomarker discovery and cell signaling analysis using single-cell transcriptomics data sets.