LDCT-to-SDCT as a Bridge Problem: Single-Step Residual Endpoint Flow Matching for Real-Time Denoising

Diffusion models achieve high reconstruction quality in low-dose computed tomography (LDCT), but their iterative sampling trajectories impose substantial computational costs. Unlike unconditional generation, paired LDCT reconstruction starts from an image that already contains the anatomy and spatial structure of the standard-dose CT (SDCT) target; reconstruction primarily requires correcting dose-related noise and artifacts. We therefore introduce Residual Endpoint Flow Matching (REFM), an LDCT reconstruction method that learns to transport an LDCT image directly toward its paired SDCT endpoint rather than defining a noise-to-image trajectory. REFM predicts the residual velocity along linear interpolations between both images and supports single-step and multi-step reconstruction using the same trained network. We evaluate five model capacities using 1 to 50 Euler steps against deterministic U-Net and diffusion-based baselines. Across all REFM variants, one-step inference consistently provides the highest reconstruction quality. On the TCIA validation set, REFM Base achieves 50.98 dB PSNR and 0.9865 SSIM at 94.54 fps, compared with 50.92 dB, 0.9847, and 9.26 fps for DDPM-10. REFM Small retains 50.71 dB while increasing throughput to 198.56 fps. Without fine-tuning, REFM Base also matches the 25-step DDPM baseline on the external Mayo Clinic dataset, although DDPM remains stronger on synthetically degraded CRLM images. Thus, our results show that exploiting paired anatomical correspondence enables diffusion-level LDCT reconstruction with a single step reconstruction.