Systematic stopping criterion for extrapolative CPF-DDNM sampling

Develop a systematic stopping criterion for CPF-DDNM reverse diffusion sampling that uses the residual trajectory to identify favorable terminal iterates, given that the iteration with the smallest data residual does not necessarily yield the best image-quality metrics.

Background

The ablation study evaluates constant and time-dependent fusion coefficients for CPF-DDNM in sparse-view CT reconstruction. Extrapolative choices of the fusion coefficient can produce oscillations in image-quality metrics during the final reverse-diffusion steps. Although the squared data residual generally decreases, the final iterate may fall in an unfavorable phase of these oscillations, and the lowest-residual iterate need not correspond to the reconstruction with the best SSIM, LPIPS, or PSNR. The authors therefore identify the absence of a principled rule for selecting a favorable terminal iterate as an unresolved methodological issue.

References

For some extrapolative configurations, however, the last reverse iteration may occur during an unfavorable phase of the oscillatory dynamics, leading to worse image-quality metrics than those obtained at the preceding iteration. Interestingly, the validation experiments showed that the iteration with the smallest data residual did not necessarily correspond to the best image-quality metrics. This observation suggests that the residual trajectory may contain useful information for identifying favorable terminal iterates, although the design of a systematic stopping criterion is left for future work.

— Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures  (2610.03261 - Morotti et al., 2 Oct 2026) in Section 4.2, “Ablation Study on the Fusion Coefficient” (paragraph following Figure 5)