ReCo-Diff: residual-conditioned deterministic sampling for cold diffusion in sparse-view CT

Abstract Objective. Sparse-view computed tomography (CT) reduces radiation dose and acquisition time but introduces structured streak artifacts that make reconstruction severely ill-posed. Cold-diffusion approaches can model such deterministic degradation processes, but existing sampling strategies may rely on scalar similarity criteria and predefined thresholds to trigger sample-adaptive resets of the degradation-level trajectory. We aim to replace this threshold-based sampling control with spatially resolved residual conditioning. Approach. We propose ReCo-Diff, a residual-conditioned cold-diffusion framework for sparse-view CT reconstruction. At each reverse step, a zero-residual baseline prediction is re-degraded using the CT degradation operator, and the resulting signed image-domain re-degradation discrepancy is used as a spatial conditioning map for a second restoration pass. ReCo-Diff does not require an adaptive reset during residual-conditioned sampling and instead follows a predetermined degradation schedule. A one-time level transition is additionally used for highly sparse inputs. The method was evaluated on the AAPM Low-Dose CT dataset under 18-, 36-, and 72-view settings using a patient-wise split with one held-out test volume. Main results. ReCo-Diff achieved PSNR values of 38.54, 42.57, and 46.98 dB at 18, 36, and 72 views, respectively. At 18 views, matched-computation analysis showed that ReCo-Diff achieved 38.54 dB compared with 38.25 dB for a two-pass zero-residual control under the same 18-NFE budget. A spatially shifted-residual control achieved 37.65 dB, indicating that effective residual conditioning benefits from spatial correspondence with the current degraded state. Significance. ReCo-Diff replaces adaptive trajectory control with step-wise spatial residual conditioning in deterministic cold diffusion. Matched-computation analysis shows that the reconstruction benefit depends on spatially aligned residual information rather than on the additional network evaluation alone. The proposed strategy provides an alternative approach to controlling error propagation under a predetermined degradation schedule without relying on sample-adaptive reset decisions.