Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures

Elena Morotti; Davide Evangelista; Elena Loli Piccolomini

cs.CVOct 2, 2026

Consecutive Posterior Fusion for Diffusive Recovery of Unobservable Image Structures

Authors: Elena Morotti, Davide Evangelista, Elena Loli Piccolomini

Organizations: Department of Computer Science and Engineerin University of Bologna Bologna, 40126, Italy

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.

Figures & tables

Figure 1: Geometric interpretation of the CPF-DDNM fusion in the extrapolative regime $\beta_{t}>1$ . The current and preceding null-space estimates $\mathcal{P}_{\operatorname{Ker}}\hat{\bm{x}}_{0|t}$ and $\mathcal{P}_{\operatorname{Ker}}\hat{\bm{x}}_{0|t+\Delta t}$ determine the direction $\bm{d}_{t}:=\mathcal{P}_{\operatorname{Ker}}\hat{\bm{x}}_{0|t+\Delta t}-\mathcal{P}_{\operatorname{Ker}}\hat{\bm{x}}_{0|t}$ . CPF-DDNM extends the estimate beyond $\mathcal{P}_{\operatorname{Ker}}\hat{\bm{x}}_{0|t+\Delta t}$ through the additional contribution $\bm{m}_{t}:=(\beta_{t}-1)\bm{d}_{t}$ , while the measurement-determined component $\bm{K}^{\dagger}\bm{y}$ remains unchanged.

Panel of Figure 2 — Figure 2: Representative axial CT images from the Mayo Clinic dataset used as ground-truth references. The second row shows zoomed regions of interest.

	Method	SSIM ( $\uparrow$ )	LPIPS ( $\downarrow$ )	PSNR ( $\uparrow$ )
$G_{30}$	FBP	$0.407\pm 0.014$	$0.442\pm 0.016$	$22.83\pm 0.46$
	SIRT	$0.636\pm 0.021$	$0.384\pm 0.014$	$26.52\pm 0.55$
	$\ell_{2}$ -TV	$0.828\pm 0.009$	$0.132\pm 0.015$	$30.61\pm 0.48$
	DPS	$0.756\pm 0.018$	$0.136\pm 0.024$	$26.62\pm 0.72$
	PS+	$0.524\pm 0.018$	$0.231\pm 0.013$	$19.96\pm 0.52$
	DiffPIR	$0.851\pm 0.012$	$0.085\pm 0.011$	$32.12\pm 0.62$

Table 1: Quantitative evaluation metrics computed over the entire test set across five runs with different initial noise realizations, for acquisition geometries with 30, 45, and 60 projection angles. In bold, the best results for each experiment.

Panel of Figure 3 — Figure 3: Qualitative comparison of sparse-view CT reconstructions obtained with the different methods. From top to bottom, the results correspond to 30, 45, and 60 projection angles. For each acquisition setting, the second row shows magnified details of the corresponding reconstructions.

Panel of Figure 4 — Figure 4: Quantitative and qualitative comparison for the 45-view sparse-CT geometry. The boxplots show the distributions of SSIM and LPIPS values computed over the entire test set across five runs with different initial noise realizations. Representative reconstructions and enlarged regions of interest are shown for visual comparison.

Panel of Figure 5 — Figure 5: Evolution of SSIM, LPIPS, PSNR, and the squared data residual along the reverse diffusion trajectory for different constant coefficients and time-dependent schedules of $\beta_{t}$ . Results refer to sparse-view CT reconstruction with $45$ projection angles.

Panel of Figure 6 — Figure 6: Robustness to measurement noise in low-dose CT reconstruction. The upper part reports the mean SSIM and LPIPS values over the complete test set for noise levels $\delta=0.1$ , $0.3$ , and $0.5$ , with whiskers indicating the corresponding standard deviations. The lower part presents representative reconstructions and enlarged regions of interest for $\delta=0.3$ , comparing the preservation of anatomical structures and fine details across the considered methods.

Noise	Method	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$
$\delta=0$	DPS	$0.497\pm 0.055$	$0.288\pm 0.017$	$19.60\pm 1.28$
	PS+	$0.774\pm 0.049$	$0.117\pm 0.015$	$28.40\pm 1.66$
	DiffPIR	$0.863\pm 0.028$	$0.093\pm 0.014$	$30.18\pm 1.32$
	DDNM	$0.856\pm 0.031$	$\bm{0.076\pm 0.014}$	$\bm{31.40\pm 1.60}$
	CPF-DDNM	$\bm{0.872\pm 0.028}$	$0.101\pm 0.014$	$31.35\pm 1.60$
$\delta=0.01$	DPS	$0.495\pm 0.055$	$0.288\pm 0.017$	$19.60\pm 1.28$

Table 2: Quantitative comparison for

\times 4

super-resolution in the noiseless setting and with noise level

\delta=0.01

. Results are reported as mean

\pm

standard deviation over the test images, after averaging each metric over five random initializations per image. Bold values indicate the best result for each setting.

Panel of Figure 7 — Figure 7: Qualitative comparison of the different methods for $\times 4$ super-resolution in the presence of measurement noise with $\delta=0.01$ . Two representative images from the test set are shown together with the corresponding reconstructions and enlarged regions of interest.

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