scChord: A Probabilistic Manifold Rectification Framework for RNA-to-Protein Translation

Measuring single-cell protein abundance is essential for resolving biological mechanisms and disease progression with high resolution. However, due to the high costs and antibody throughput limitations of current proteomics, inferring protein levels from readily available RNA data has become a critical computational necessity. Existing regression and generative methods face a fundamental geometric bottleneck: enforcing deterministic constraints on noisy, heteroscedastic data collapses intrinsic uncertainty into a rough latent manifold, which destabilizes the learning process. To overcome this, we present scChord, a noise-decoupled conditional flow matching framework built on Probabilistic Manifold Rectification. Our approach utilizes a probabilistic decoder to disentangle technical noise and over-dispersion from the raw counts, absorbing them into distributional parameters. This allows the rectified latent manifold to focus more on biological signals, serving as a robust geometric regularizer for learning efficient transport trajectories. Extensive experiments on multiple multi-omics benchmarks demonstrate that scChord not only achieves state-of-the-art inference accuracy but also faithfully reconstructs high-fidelity biological heterogeneity and complex protein distributions.