Mixed Prior Diffusion Posterior Sampling for High Resolution CT Reconstruction

Abstract

Diffusion models have a demonstrated ability to estimate complex prior distributions, including classes of image data. Diffusion Posterior Sampling (DPS) has recently emerged as a powerful framework for incorporating such learned priors into inverse problems; however, the performance of DPS is limited by the ability to train high-quality priors. This is particularly true in x-ray computed tomography, where patient data must balance noise and spatial resolution within acceptable x-ray dose limits. In this work, we propose Mixed Prior Diffusion Posterior Sampling (Mixed Prior DPS) that integrates global and local diffusion priors in the reconstruction. The global diffusion model is trained on full CT volume with modest spatial resolution to capture large-scale anatomical structures and lower frequency content. A local diffusion model trained on high-resolution patches focuses on fine-scale, high-frequency details. The two priors are combined in the Fourier domain to form a mixed posterior mean, and a masking strategy is employed to apply prior mixing selectively within an appropriate local region-of-interest while employing standard-resolution DPS elsewhere. This framework permits the use of modest resolution CT datasets for global context in conjunction with specialized high-resolution datasets (e.g. organ or tissue specific scans based on specialized protocols or on ex vivo samples where high-resolution, low-noise images can be collected without radiation dose constraints). In this work, we created a high-resolution lung training dataset for the local prior model using a CBCT benchtop system and a (plastinated) physical lung specimen. Experimental results on simulated low-dose CT demonstrate that the proposed method improves spatial resolution and data consistency as compared with filtered backprojection, standard DPS, and DPS with resampling, while preserving fine lung structures. These results highlight the effectiveness of multi-resolution prior integration for low-dose CT reconstruction.

I. Introduction

Diffusion models [1]–[3] have demonstrated remarkable performance in generative modeling tasks and have recently been applied to inverse problems through diffusion posterior sampling (DPS). [4] A key advantage of DPS is that a prior model can be learned through one-time unsupervised training and subsequently applied to a wide range of measurement models without retraining. This flexibility makes DPS particularly well suited for x-ray computed tomography (CT) reconstruction, where imaging protocols can vary substantially across patients and scanners, including differences in tube current, scan geometry, axial coverage, and pitch. Recent studies have demonstrated the effectiveness of DPS for CT reconstruction across diverse imaging protocols [5], and several acceleration strategies have been proposed to enable efficient processing of clinically sized datasets [6]–[8]. Together, these developments highlight DPS as a promising and data-efficient reconstruction framework.

Despite these advantages, DPS performance is fundamentally limited by the availability and quality of training data. In particular, large-scale high-resolution CT datasets are difficult to obtain in clinical settings, and existing high-resolution scans are often noisy, making them suboptimal for training diffusion priors. As a result, most diffusion-based CT priors are trained on standard clinical datasets that provide modest spatial resolution. Although such data are effective for capturing global anatomical structure, they offer limited support for reconstruction methods that seek to enhance spatial resolution beyond current clinical standards. Existing strategies to address this limitation include super-resolution preprocessing of training data [9]–[11] or the incorporation of priors trained on general-purpose image datasets. However, these approaches are only indirectly related to the true high-resolution anatomical features that may be present in CT images.

To address this challenge, we consider an alternative paradigm in which a clinically derived, nominal-resolution anatomical prior is incorporated but additional high-resolution prior information is introduced from a complementary dataset. For example, public clinical CT databases can provide abundant full-field anatomical data, while microCT or specialized high-resolution scans of ex vivo organs or tissue samples can offer much better structural detail for specific anatomical regions with low noise since there are no patient dose constraints. Such high-resolution priors are region-dependent since fine-scale anatomical structures can vary significantly across organs and tissue types. Thus, we employ strategies to apply tissue-specific priors in appropriate anatomical regions of interest. This combination has the potential to provide a globally consistent anatomical prior together with region-specific high-resolution information, enabling improved reconstruction in targeted regions of interest (ROIs).

Our proposed approach is called Mixed Prior Diffusion Posterior Sampling (Mixed Prior DPS) and integrates both global and local diffusion priors for low-dose CT reconstruction. The method employs a global diffusion model trained on full-field, nominal-resolution CT images to capture large-scale anatomical structure and low-frequency content, alongside a patch-based diffusion model trained on high-resolution local image patches to model fine-scale, high-frequency details. These two priors are combined through a frequency-domain fusion strategy, and a masking mechanism is used to selectively apply the mixed prior within appropriate anatomical ROIs while maintaining global consistency elsewhere. We develop a mathematical formulation of the proposed approach and present an efficient algorithm for posterior sampling with mixed priors. Simulation results demonstrate that the proposed method is stable and effectively utilizes complementary information from both priors, enabling enhanced regional spatial resolution while preserving data consistency.

II. Methodology

A. Diffusion Posterior Sampling

1). Diffusion Model:

A diffusion model is commonly formulated using a stochastic differential equation (SDE) [2], which progressively transforms the real data distribution $p_{\mathit{\text{data}}}\left(x\right)$ into a standard Gaussian distribution $N(0,I)$. In particular, the variance-preserving forward SDE is defined as

$$dx=-\frac{1}{2}\beta \left(t\right)xdt+\sqrt{\beta \left(t\right)}dw,$$ (1)

where $\beta \left(t\right)$ denotes a predefined noise schedule and $w$ represents Brownian motion.

The time-dependent score function ${\nabla }_{x_t}\text{log}{p}_t\left(x_t\right)$ is approximated by a neural network $s_{\theta }\left(x_t,t\right)$. Starting from Gaussian noise, generative samples are obtained by evolving the system toward the data distribution using the corresponding reverse-time SDE,

$$dx=\left[-\frac{1}{2}\beta (t)x-\beta (t)s_{\theta }\left(x_t,t\right)\right]dt+\sqrt{\beta (t)}d\bar{w}.$$ (2)

2). Diffusion Posterior Sampling:

Conditional posterior sampling can be achieved by modifying the unconditional score in reverse SDE in (2) to the conditional score ${\nabla }_{x_t}\text{log}{p}_t\left(x_t|y\right)$, where $y$ denotes the measurement data. Applying Bayes’ rule, the conditional score can be decomposed into the sum of the unconditional score and the gradient of the log-likelihood:

$${\nabla }_{x_t}\text{log}{p}_t\left(x_t|y\right)={\nabla }_{x_t}\text{log}{p}_t\left(x_t\right)+{\nabla }_{x_t}\text{log}{p}_t\left(y|x_t\right).$$ (3)

The unconditional score ${\nabla }_{x_t}\text{log}{p}_t\left(x_t\right)$ is approximated by the neural network $s_{\theta }\left(x_t,t\right)$. To approximate the likelihood gradient term, Chung et al. [4] proposed replacing the time-dependent variable $x_t$ in the likelihood $\text{log}{p}_t\left(y|x_t\right)$ with the posterior mean ${\hat{x}}_{0,t}$. This posterior mean is computed using Tweedie’s formula:

$${\hat{x}}_{0,t}=\mathbb{E}\left[x_0|x_t\right]=\frac{1}{\sqrt{\bar{\alpha }\left(t\right)}}\left(x_t+(1-\bar{\alpha }(t\left)\right)s_{\theta }\left(x_t,t\right)\right)$$ (4)

Substituting the resulting conditional score into the reverse SDE yields “standard” Diffusion Posterior Sampling (DPS).

3). Acceleration Strategies for DPS:

To accelerate DPS, we adopt several efficiency strategies proposed in previous work [6]. First, a jump-start initialization is used to initialize the reverse diffusion process from a filtered backprojection (FBP) reconstruction rather than pure Gaussian noise. The FBP image provides informative structural priors at minimal computational cost. Although FBP reconstructions in low-dose or sparse-view settings may contain artifacts, effective initialization only requires a reasonable approximation of the image in the forward process. Specifically, Gaussian noise is added to the FBP reconstruction as

$$x_{\text{FBP},t}=\sqrt{\bar{\alpha }\left(t\right)}{x}_{\text{FBP}}+\sqrt{1-\bar{\alpha }\left(t\right)}ϵ.$$ (5)

where $ϵ~N(0,I)$. For a sufficiently large initialization time $t_0$, the FBP image after adding Gaussian noise approximates the distribution of $x_{t_0}$,

$$x_{\text{FBP},t_0}\approx x_{t_0}~N(\sqrt{\bar{\alpha }\left(t_0\right)}{x}_0,\left(1-\bar{\alpha }\left(t_0\right)\right)I).$$ (6)

By the Markov property of diffusion models, the reverse process can therefore be initialized at $t_0$, skipping early diffusion steps and significantly reducing sampling time while maintaining stability and reconstruction quality.

Other strategies in [6] including gradient approximation, and accelerated optimization are also employed for efficient DPS computation.

B. Mixed Prior Diffusion Posteior Sampling

1). Global Prior Model and Local Prior Model:

We employ two diffusion models to estimate the anatomical prior distribution. The global prior model is trained on full CT images and is used to capture the global data distribution. This model primarily captures large-scale information, including overall anatomy, object boundaries, and low-frequency image content.

The local prior model is trained separately on high-resolution image patches extracted from tissue specifc ROIs, such as the lung. By focusing on localized patches rather than full images, this model emphasizes fine-scale, high-frequency details that are often blurred or ignored in the global diffusion model.

Together, these two priors provide complementary information during reconstruction. The global prior enforces anatomical consistency and structural coherence, while the local prior enhances detailed textures and fine structures.

2). Histogram-Based Intensity Normalization:

The global and local diffusion priors may be trained on CT datasets acquired under different imaging conditions, including variations scanning protocols, beam quality, corrections, etc. Consequently, the attenuation coefficient distributions of the two datasets may differ, introducing a domain shift that can hinder effective integration of the priors during posterior sampling.

To address this issue, we perform a histogram-based distribution alignment to match the intensity statistics of the global and local datasets. This preprocessing step preserves relative contrast while aligning the overall intensity range and statistical properties. By operating in a consistent intensity space, the global and local diffusion priors can be better combined during posterior sampling. We have observed that this alignment improves stability and convergence, enabling effective fusion of global anatomical structure with local high-resolution detail.

3). Prior Mixing:

We employ two prior models within the high-resolution ROI to guide reconstruction by jointly estimating the posterior mean of the ROI. To integrate information from both priors, we combine their posterior means in the Fourier domain, where the global prior contributes low-frequency components and the local prior contributes high-frequency details. Specifically, the mixed posterior mean ${\hat{x}}_{0,\text{mixed}}$ is defined as

$${\hat{x}}_{0,\text{mixed}}={ℱ}^{-1}\left(ℒ\left(ℱ\left({\hat{x}}_{0,\text{global}}\right)\right)+\mathscr{H}\left(ℱ\left({\hat{x}}_{0,\text{local}}\right)\right)\right)$$ (7)

where ${\hat{x}}_{0,\text{global}}$ and ${\hat{x}}_{0,\text{local}}$ denote the posterior means of ROI predicted by the global and local diffusion models, respectively; $ℱ$ and ${ℱ}^{-1}$ denote the Fourier and inverse Fourier transforms; and, $ℒ(·)$ and $\mathscr{H}(·)$ represent the low-pass and high-pass filters, respectively. This mixing allows each prior to operate at the spatial scale where it is most reliable, combining global structural consistency with locally detailed texture.

Directly mixing posterior means in the Fourier domain may introduce inconsistencies that accumulate during the reverse diffusion process and lead to unstable sampling. To solve this problem, we use a resampling [12] step after each likelihood update during posterior sampling. This resampling ensures that samples are drawn from a marginal distribution conditions on the current posterior mean, preventing error accumulation and stabilizing the reconstruction process.

4). Region-Dependent Prior Mixing with Masked DPS:

During posterior sampling, prior mixing is applied only within the ROI for which the high-resolution prior is available, while DPS using only the global diffusion model is retained for the remaining image regions. This region-dependent prior estimation is enforced using a binary masking method, following the approach in [13]. Specifically, a binary mask $M\in \{\mathrm{0,1}{\}}^{H\times W}$ is constructed to extract the ROI from the image, where $M(i,j)=1$ indicates pixels located inside the ROI and 0 otherwise. At each posterior sampling step, the posterior mean of the full image is updated by combining the ROI-specific update with the global update as

$${\hat{x}}_0=M\odot {\hat{x}}_{0,\text{mixed}}+(1-M)\odot {\hat{x}}_{0,\text{global}}$$ (8)

where ${\hat{x}}_{0,\text{mixed}}$ is computed using the mixed prior that combines global and local patch-based diffusion models, and ${\hat{x}}_{0,\text{global}}$ is obtained from the global diffusion model. While patch-based training alone may not provide sufficient global coherence, this limitation is effectively addressed in our reconstruction process. In particular, the physical measurement model enforced through the likelihood term and the global structural constraints imposed by the global diffusion prior.

In addition to the frequency-domain prior mixing described above, we introduce a temporal prior mixing strategy that operates across reverse diffusion time steps. During the reverse sampling process, the choice of prior model for computing the score function is region-dependent. Outside the ROI, the global diffusion model is used exclusively to compute the score at every time step. Within the ROI, however, the global and local diffusion models are alternately employed at different reverse sampling time steps. This alternating scheme allows the reconstruction within the ROI to benefit from both the global prior, which provides large-scale structural coherence and anatomical consistency, and the local prior, which contributes fine-scale, high-frequency detail. By inter-leaving the two priors temporally, this strategy complements the frequency-domain mixing of posterior means, offering an additional mechanism to integrate multi-resolution prior information throughout the reverse diffusion process. Together, the frequency-domain fusion and the temporal prior mixing enable a more comprehensive utilization of complementary prior knowledge, improving both stability and reconstruction quality within the ROI.

Additionally, the jump start strategy [6] initializes the reverse process with strong posterior restriction which significantly constrains the sampling solution space. These constraints allow the patch-based diffusion model to reliably predict local posterior means without introducing global inconsistencies. As a result, the mixed prior selectively enhances fine-scale structures within the ROI, while the global prior maintains anatomical consistency in the background, leading to improved stability, reconstruction quality, and computational efficiency during posterior sampling. The overall algorithm and pseudocode is presented in Algorithm 1.

Algorithm 1.

Mixed Prior DPS

1:	$T^{\prime }$: Jump start time step, $x_{\mathit{\text{fbp}}}$: FBP reconstruction, $A,y$: Forward projector and measurement
2:	$\eta$: Step size, $N$: Number of iteration per reverse step, $m=0,v=0$: First moment vector and second moment vector, ${\gamma }_1=0.9,{\gamma }_2=0.999$: Adam momentum coefficients
3:	${\beta }_t,{\alpha }_t,{\sigma }_t$ and ${\bar{\alpha }}_t$: Scheduler, where ${\alpha }_i=1-{\beta }_i,{\sigma }_t={\beta }_t$ and ${\bar{\alpha }}_i={\prod }_{j=1}^i{\beta }_i$.
4:	$M$: The mask of the ROI.
5:	$x_{T^{\prime }}=\sqrt{{\bar{\alpha }}_{T^{\prime }}}{x}_{\text{FBP}}+\sqrt{1-{\bar{\alpha }}_{T^{\prime }}}ϵ,ϵ~N(0,I)$
6:	for $t=T^{\prime }$ to 1 do:
7:	${\hat{x}}_{0,\text{global}}=\frac{1}{{\sqrt{\bar{\alpha }}}_t}\left(x_t+\left(1-{\bar{\alpha }}_t\right){ϵ}_{\theta ,\text{global}}\left(x_t,t\right)\right)$
8:	${\hat{x}}_{0,\text{local}}=M\odot \left(\frac{1}{{\sqrt{\bar{\alpha }}}_t}\left(x_t+\left(1-{\bar{\alpha }}_t\right){ϵ}_{\theta ,\text{local}}\left(x_t,t\right)\right)\right)$
9:	${\hat{x}}_{0,\text{mixed}}={ℱ}^{-1}\left(ℒ\left(ℱ\left(M\odot {\hat{x}}_{0,\text{global}}\right)\right)+\mathscr{H}\left(ℱ\left({\hat{x}}_{0,\text{local}}\right)\right)\right)$
10:	${\hat{x}}_0=M\odot {\hat{x}}_{0,\text{mixed}}+(1-M){\hat{x}}_{0,\text{global}}$
11:	for $i=1$ to $N$ do:
12:	${\hat{x}}_0=\text{Adam}\left({\hat{x}}_0,{\nabla }_{{\hat{x}}_0}{‖y-B\text{exp}\left(-A{\hat{x}}_0\right)‖}_{\mathbf{2}}^2,\eta ,{\gamma }_1,{\gamma }_2\right)$
13:	end for
14:	$x_t^{\prime }=\sqrt{{\bar{\alpha }}_t}{\hat{x}}_0+\sqrt{1-{\bar{\alpha }}_t}\xi ,\xi ~N(0,I)$
15:	$z~N(0,I)$
16:	if $t$ is odd then
17:	${ϵ}_{\theta }\left(x_t^{\prime },t\right)=M\odot {ϵ}_{\theta ,\text{global}}\left(x_t^{\prime },t\right)+(1-M)\odot {ϵ}_{\theta ,\text{local}}\left(x_t^{\prime },t\right)$
18:	else
19:	${ϵ}_{\theta }\left(x_t^{\prime },t\right)={ϵ}_{\theta ,\text{global}}\left(x_t^{\prime },t\right)$
20:	end if
21:	$x_{t-1}=\frac{1}{\sqrt{{\alpha }_t}}\left(x_t^{\prime }-\frac{1-{\alpha }_t}{\sqrt{1-{\bar{\alpha }}_t}}{ϵ}_{\theta }\left(x_t^{\prime },t\right)\right)+{\sigma }_{t}z$
22:	end for

III. Experiments

A. Network Training and Data Acquisition

We employed a U-Net architecture [14] with an attention layer at the bottleneck to estimate both the global and local prior distributions. The diffusion models follow the DDPM framework [1] with a linear noise schedule defined by ${\beta }_1=0.0001$ and ${\beta }_T=0.02$.

The global diffusion models were trained on the CT Lymph Nodes dataset [15]. The full image size is 512 × 512 with a voxel size of 0.75 mm. The training data were Fourier upsampled to 1024 × 1024 grids to match the high-resolution reconstruction. We selected the lung as the high-resolution ROI target for local diffusion model training and created lung masks using open source lung segmentation tool [16]. The high-resolution dataset used for training the local diffusion model was acquired using a flat-panel, cone-beam CT (CBCT) bench by scanning a plastinated lung. CBCT data were collected using 120 kVp, 120 mAs, and 1280 views. The detector pixel size was 0.2 mm × 0.2 mm, and the voxel size was 0.25 mm × 0.25 mm × 0.25 mm. Training patches of size 64 × 64 were extracted from multiple reconstructed volumes with a size of 30 × 1024 × 1024. The training samples from two datasets are presented in Fig. 1.

Fig. 1:

Illustration of samples from global training dataset and local training dataset. The top row shows samples from global dataset. The bottom row shows samples from local dataset.

B. Low-Dose CT Reconstruction and Hyper-parameters

We use the proposed Mixed Prior DPS to perform low-dose CT reconstruction. We adopt a standard monoenergetic CT system model, $y=I_0\text{exp}(-Ax)$, where $A$ is the linear forward projection matrix, $I_0$ is the incident photon intensity, and $y$ denotes the measured data.

For evaluation, we scanned a body phantom with a plastinated lung inserted using our CBCT bench system to simulate a high-resolution scan. The scan parameters were 120 kVp, 10 ms, and 30 mA. The reference image was obtained by averaging four independent scans. Low-dose CT data were simulated by applying binomial thinning to the Poisson-distributed photon counts with $p=0.5$, corresponding to half the dose of a single scan. The proposed Mixed Prior DPS was then evaluated on the resulting low-dose CT reconstruction.

The CT system geometry uses a source-to-axis distance of 872.96 mm and a source-to-detector distance of 1351.3 mm, with a detector pixel size of 0.278 mm, voxel size of 0.35 mm and 1080 views covering 360°. We compare the proposed Mixed Prior DPS with filtered backprojection (FBP), standard DPS [4], and standard DPS with resampling [12]. The hyperparameters in the acceleration strategies [7] for all methods, including the jump-start parameter $T\prime$, the maximum-likelihood optimizer step size $\eta$, and the number of optimizer iterations per step $N$, are fine-tuned as follows: (i) Standard DPS: $T\prime =30,\eta =4\times {10}^{-5},N=14$; (ii) Standard DPS with resampling: $T\prime =30,\eta =2\times {10}^{-4},N=24$; (iii) Mixed Prior DPS: $T\prime =30,\eta =2\times {10}^{-4},N=24$.

IV. Results

The reconstruction results are presented in Fig. 2. Compared with the baseline methods, the proposed Mixed Prior DPS achieves improved spatial resolution and better data consistency in the reconstructed images. In particular, fine anatomical structures within the lung region are more clearly resolved, with sharper boundaries and reduced noise. In contrast, standard DPS exhibits noticeable noise and blurry, while DPS with resampling tends to oversmooth high-frequency details. These results demonstrate that combining global and local priors enables Mixed Prior DPS to better balance structural fidelity and detail preservation in low-dose CT reconstruction.

Fig. 2:

Illustration of Mixed Prior DPS with comparisons to FBP, “standard” DPS, and DPS with resampling. The first rows shows different reconstructions of the plastinated lung. The bottom two rows show zoomed areas of the lung.

We evaluated image quality using quantitative metrics, including root-mean-square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM), for the proposed Mixed Prior DPS and the comparison methods. As summarized in Fig. 2 the first row, Mixed Prior DPS achieves the lowest RMSE and the highest PSNR and SSIM among all methods. Specifically, Mixed Prior DPS reduces RMSE compared with standard DPS and DPS with resampling, while improving PSNR and SSIM, indicating enhanced reconstruction accuracy and data consistency.

V. Conclusion

We proposed Mixed Prior Diffusion Posterior Sampling, a reconstruction method that integrates global and local diffusion priors for low-dose CT reconstruction. By combining a global diffusion model trained on full-size, nominal-resolution CT images with a local diffusion model trained on high-resolution patches, the proposed method leverages complementary prior information. The frequency-domain fusion strategy and temporal prior mixing enable effective integration of low-frequency anatomical structure with high-frequency detail, while the masked DPS ensures that high-resolution enhancement is applied selectively within targeted anatomical regions. Experimental results on low-dose CT data reconstruction demonstrate that Mixed Prior DPS achieves improved spatial resolution, reduced noise, and better data consistency compared with FBP, standard DPS, and DPS with resampling. This method offers a flexible paradigm for incorporating specialized high-resolution datasets, such as those acquired from ex vivo specimens, into clinical CT reconstruction pipelines, and may be extended to other anatomical regions and imaging applications in future work.