Flow-Matching-Refined Dirichlet-Prior Autoencoders for Interpretable and Structurally Balanced Single-Cell Representation Learning

Variational autoencoders for single-cell transcriptomics typically learn Gaussian latent spaces that lack part-based interpretability: individual latent dimensions carry no inherent biological meaning and the decoder provides no explicit gene-program readout. We introduce Topic-FM, a family of neural topic VAEs in which a logistic-normal Dirichlet prior constrains the latent vector to the probability simplex, turning each coordinate into a topic proportion and the decoder weight matrix into a directly readable topic-gene signature. A conditional optimal-transport flow field, trained entirely in pre-softmax [R]K, sharpens posterior geometry without modifying the decoder or breaking simplex validity. Unlike nonparametric mixture priors that improve geometry at the expense of label concordance, Topic-FM improves all core metrics simultaneously: across 56 scRNA-seq datasets, Topic-FM-Transformer raises NMI by 8.2%, ARI by 20.4%, and ASW by 21.7% relative to prior-free Pure-VAE (composite 0.502 vs. 0.434, +15.6%). Wilcoxon signed-rank tests confirm significance with medium-to-large Cliffs{delta} effects on all three metrics--no concordance-geometry trade-off is observed. Downstream kNN classification improves by 13.5% in accuracy and 27.7% in macro-F1. Among four architectural variants, Topic-FM-Contrastive achieves the highest external core win rate (86.4% against 23 baselines), while Topic-FM-Transformer leads on composite score and supervised discrimination. Dual-pathway biological validation--perturbation importance and direct decoder-{beta} readout-- yields convergent GO enrichment, demonstrating that the learned topics correspond to coherent, annotatable gene programs rather than opaque embedding dimensions.