Yuxuan Qiu | Search arXiv

arXiv2026

CRNDiff: Count-Native Diffusion Framework via Chemical Reaction Networks

Scientific measurements such as single-cell RNA (scRNA) sequencing often take the form of nonnegative integer counts, whereas continuous-state diffusion models approximate this discrete structure using continuous coordinates. Building on stochastic chemical reaction networks (CRNs), a class of count-native Markov jump processes, we introduce CRNDiff, a structured framework that combines count-space diffusion with inference-time conditioning on rare subpopulations. An independent birth--death instantiation yields a closed-form transition kernel for forward noising. This kernel enables reverse sampling via forward-filtering backward-sampling (FFBS) and supports data-driven selection of the terminal noising time, eliminating the need for a validation sweep. This tractability also lets us introduce tilted Feynman--Kac (FK) steering, a method for sampling target subpopulations from a frozen generator without retraining. By tilting posterior marginals before FK particle correction, steering mitigates importance-weight concentration when the target population is rare. Using scRNA-seq data from the human heart cell atlas, we test the ability of CRNDiff to generate cell-type-specific distributions. Across the three evaluated target populations, CRNDiff achieves the highest conditional fidelity among the evaluated generative models, with larger mean purity margins for rarer target populations. Generated cells preserve marker-level differential-expression structure. Replacing real training cells for the target classes with generated cells yields downstream classification performance approaching that of the real-data reference.

cs.LG↗

arXiv2024

Generalized Flow Matching for Transition Dynamics Modeling

Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities. However, the computational challenge often lies on sampling exponentially many paths in which only a small fraction ends in the target metastable state due to existence of high energy barriers. To amortize the cost, we propose a data-driven approach to warm-up the simulation by learning nonlinear interpolations from local dynamics. Specifically, we infer a potential energy function from local dynamics data. To find plausible paths between two metastable states, we formulate a generalized flow matching framework that learns a vector field to sample propable paths between the two marginal densities under the learned energy function. Furthermore, we iteratively refine the model by assigning importance weights to the sampled paths and buffering more likely paths for training. We validate the effectiveness of the proposed method to sample probable paths on both synthetic and real-world molecular systems.

cs.LG↗