REFM (Residual Endpoint Flow Matching)

A low-dose CT scan and its standard-dose counterpart show the same patient, the same slice and the same geometry. The anatomy is already there; what the low dose costs is quantum noise and streak artifacts over the top of it. A denoising diffusion model applied to that problem nonetheless begins at pure Gaussian noise and spends ten to a thousand network evaluations regenerating structure it was handed at the start.

Residual Endpoint Flow Matching (REFM), from Universidad de los Andes, Chile with Universidad de Santiago de Chile, replaces that trajectory with a straight line between the two images the task already supplies: the conditional path is the linear interpolation from a low-dose image to its paired standard-dose target. Along it the velocity is constant and equal to the endpoint residual, so a time-conditioned network trained to regress that velocity can be integrated with as few as one Euler step — at which point the update collapses to adding the predicted residual directly to the input.

The result inverts the usual expectation for a generative reconstructor: across all five REFM capacities, one step gives the best image quality, not merely the cheapest, because extra integration steps accumulate error against states the network never saw in training. The catalog's closest analogue is 7TCDM, a conditional diffusion denoiser for 7T brain MRI, which transfers across scanners the same way but keeps the iterative sampler REFM discards.

#Key Features

• Paired endpoint transport: The conditional path runs between the low-dose image and its aligned standard-dose target rather than from noise, so the network only has to learn the dose-related residual instead of the anatomy.
• One network, any step count: A single checkpoint integrates with 1, 4, 8, 10, 25 or 50 Euler steps without retraining, making the quality-latency trade-off a deployment choice.
• Single-step inference is the best setting: REFM Base loses 0.93 dB PSNR going from one step to fifty, and the same trend holds across every capacity.
• A five-point capacity ladder: Base (113.67M parameters) down to Tiny (19.36M), all sharing one architecture and differing only in channel width and residual depth.
• Transfers without fine-tuning: The TCIA-trained checkpoint was applied unchanged to paired quarter-dose scans from a different institution and matched a 25-step diffusion baseline.

#Technical Details

Every variant is a time-conditioned U-Net over single-channel 256 × 256 slices, with six encoder and decoder stages, symmetric skip connections, and self-attention at one deep resolution and at the bottleneck; sinusoidal time embeddings passed through a learned MLP condition each residual block. Channel widths run 128–256–512 for Base down to 64–128–256 for Tiny. Training used the TCIA Low Dose CT and Projection dataset — 120 patients (45 chest, 36 brain, 39 liver) with an independent 30-patient validation partition.

On that validation set, one-step REFM Base reaches 50.98 dB PSNR and 0.9865 SSIM at 94.54 images per second, against 50.92 dB, 0.9847 and 9.26 fps for a 10-step conditional DDPM trained on the same partition — roughly 10.2× the throughput at equal quality — and against 42.87 dB for a plain U-Net regressor. REFM Small holds 50.71 dB at 198.56 fps, and Tiny reaches 338.02 fps for a 1.19 dB reduction. Per region, Base reaches 63.53 dB on brain, 54.74 dB on liver and 43.68 dB on chest; chest is the hardest subset for every method and the one where REFM beats DDPM-10 outright on both metrics. Held-out transfer to ten paired Mayo Clinic Grand Challenge cases gives 48.83 dB and 0.9866 SSIM, effectively equivalent to 25-step DDPM.

#Applications

The target use is clinical CT at reduced radiation dose: acquire at a low-dose protocol and restore standard-dose appearance fast enough for volumetric reconstruction and on-table review. The capacity ladder matters here — Tiny's 338 fps makes whole-volume processing feasible on modest hardware, the constraint that usually keeps diffusion reconstructors in the research setting. Sites without paired training data of their own are the other beneficiary, since one checkpoint carried across institutions unchanged.

#Impact

REFM's contribution is a reframing rather than a quality gain: it preserves diffusion-level fidelity at roughly a tenth of the sampling cost, and it argues that paired restoration never needed a noise-to-image trajectory in the first place. The evidence carries clear boundaries. On CRLM images degraded synthetically with a Poisson–Gaussian noise model, 25-step DDPM stays ahead of every REFM variant, so direct paired transport is sensitive to the degradation process it was trained against. The U-Net baseline is not capacity-matched, leaving the contribution of time-conditioned intermediate supervision unisolated, and reported throughput measures the sampler alone, excluding preprocessing and volume assembly. PSNR and SSIM are also not measures of diagnostic fidelity — patient-level, task-based and volumetric evaluation is still outstanding. The work is a preprint awaiting peer review, and neither code nor trained weights have been released; the authors offer study data on request.