Abstract
Solving severely ill-posed imaging inverse problems requires recovering image structures that are unobservable or weakly constrained by the measurements. Diffusion models provide expressive learned priors for inferring such missing information, while posterior sampling incorporates measurement consistency along the reverse process. Standard diffusion posterior samplers, however, rely on instantaneous measurement-aware estimates, without explicitly exploiting information carried by previous posterior corrections. We introduce Consecutive Posterior Fusion Denoising Diffusion Null-Space Models (CPF-DDNM), an inference-time strategy that fuses consecutive measurement-aware estimates to improve the diffusive recovery of unobservable image structures, without requiring retraining or additional denoiser evaluations. We instantiate this principle within DDNM, whose range/null-space decomposition reveals that consecutive fusion preserves the measurement-determined component while acting exclusively on the prior-driven null-space estimate. We thus provide a geometric interpretation of CPF-DDNM and a local error analysis that characterizes the optimal time-dependent fusion coefficient, including the extrapolative regime. Experiments on sparse-view and simulated low-dose computed tomography, as well as medical image super-resolution, show consistent improvements over DDNM and competitive performance against diffusion-based inverse solvers.
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Publication details
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- Green open access
Cite this article
APA 7
Morotti, E., Evangelista, D., & Piccolomini, E. L. (2026). Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures. https://omanscience.com/en/articles/consecutive-posterior-fusion-for-diffusive-recovery-of-unobservable-image-structures
MLA 9
Morotti, Elena, et al. "Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures." https://omanscience.com/en/articles/consecutive-posterior-fusion-for-diffusive-recovery-of-unobservable-image-structures.
Chicago (author–date)
Morotti, Elena, Davide Evangelista, and Elena Loli Piccolomini. 2026. "Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures." https://omanscience.com/en/articles/consecutive-posterior-fusion-for-diffusive-recovery-of-unobservable-image-structures.
Harvard
Morotti, E., Evangelista, D. and Piccolomini, E. L. (2026) 'Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures', Available at: https://omanscience.com/en/articles/consecutive-posterior-fusion-for-diffusive-recovery-of-unobservable-image-structures.
Vancouver
Morotti E, Evangelista D, Piccolomini EL. Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures. https://omanscience.com/en/articles/consecutive-posterior-fusion-for-diffusive-recovery-of-unobservable-image-structures
IEEE
E. Morotti, D. Evangelista, and E. L. Piccolomini, "Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures," https://omanscience.com/en/articles/consecutive-posterior-fusion-for-diffusive-recovery-of-unobservable-image-structures.