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EPC-RawDC: Equivariant Physics Constrained 3D Diffusion with Raw Data Consistency for CBCT to CT Image Synthesis

Alzahra Altalib, Chunhui Li, Alessandro Perelli

arXiv:2610.40046v1cs.CVcs.AIphysics.med-ph

TL;DR

CBCT’s quantitative use is limited by image degradations, while image-driven synthesis does not ensure consistency with acquisition physics or scan-specific measurements. EPC-RawDC combines conditional 3D latent diffusion with geometry-derived and raw-measurement projection constraints; across two cohorts, it achieved the best mean performance among evaluated methods and reduced MAE relative to DDPM.

  • Problem

    CBCT degradations limit quantitative Hounsfield-unit use, and image-driven synthesis may not satisfy scanner geometry or the individual scan’s projection measurements.

    Source: §I · p. 1

  • Method

    EPC-RawDC combines conditional 3D latent diffusion with geometry-transformed reference projection supervision and scan-specific raw data consistency through a scanner-specific forward model.

    Source: B. Main Contributions · p. 2, §I · p. 2

  • Results

    Across SynthRAD2025 and JUST, EPC-RawDC had the best mean performance among evaluated methods, reducing mean MAE relative to DDPM by 20.3% and 19.0%, respectively.

    Source: B. Single Domain Performance and… · p. 7, §VI · p. 10

  • Takeaways & Limitations

    Across both acquisition settings, combining equivariant projection supervision with RawDC maintained consistent performance and improved agreement with projection measurements and transformed reference projections.

    Source: B. Single Domain Performance and… · p. 7, §VI · p. 10

Abstract

from arXiv · show

Cone beam computed tomography (CBCT) is widely used for image guided and adaptive radiotherapy, but scatter, noise, reconstruction artifacts, and inaccurate Hounsfield units limit its quantitative use. Recent diffusion approaches for CBCT to CT synthesis remain largely image driven, with limited use of the underlying acquisition physics. We propose EPC-RawDC, a conditional 3D latent diffusion framework that combines volumetric generative modeling with two complementary constraints derived from the same scanner specific CBCT forward model. First, geometry equivariant projection constraint exploits the rotational equivariance of the CBCT forward operator by supervising the synthesized CT through correspondingly transformed reference projections. Second, raw data consistency uses noisy projection measurements of the individual acquisition as scan specific supervision during training. The framework was evaluated on two independent clinical cohorts with distinct scanner geometries and projection sources. For JUST, the physics constraints used measured clinical raw CBCT projections acquired with an Elekta system, whereas for SynthRAD2025 the projection data were simulated from the reference CT using a Varian geometry with Poisson photon statistics. EPC-RawDC achieved an SSIM of 0.97 in both cohorts and improved PSNR over DDPM by 2.66 dB on SynthRAD2025 and 2.10 dB on JUST, while reducing mean MAE by 20.3% and 19.0%, respectively. On SynthRAD2025, projection consistency and equivariant errors were reduced by 55.0% and 41.4% relative to DDPM. These results demonstrate that combining a volumetric diffusion prior with scanner geometry and scan specific projection measurements improves quantitative CBCT to CT synthesis across both simulated and measured projection domains. Code available after publication at https://github.com/ALZAHRAALTALIB/EPC-RawDC.

I. INTRODUCTION

CBCT offers treatment-position volumetric imaging, but acquisition and reconstruction degradations limit its quantitative use. EPC-RawDC addresses the gap between image-driven synthesis and scanner- and measurement-consistent predictions.

I. INTRODUCTION

  • Scatter, noise, and reconstruction artifacts can distort Hounsfield units, limiting quantitative uses such as dose calculation and online treatment adaptation.Image similarity alone does not necessarily predict dosimetric accuracy.Source: §I · p. 1
  • Image-driven synthesis can produce plausible CT volumes without guaranteeing consistency with scanner geometry or the individual scan’s projection measurements.The acquisition trajectory and forward model provide physical structure independently of training data.Source: §I · pp. 1–2
  • Prior equivariant approaches used scanner-induced projection transformations, while EPC-RawDC adds supervision from the noisy measurements of each acquisition.The geometry-derived term uses a noise-free transformed reference projection; RawDC adds patient- and scan-specific measurement supervision.Source: §I · p. 2

A. Positioning Against Existing Methods

  • EPC-RawDC combines volumetric latent diffusion, geometry-transformed projection supervision, and scan-specific raw projection consistency in one synthesis framework.Earlier projection-consistency methods addressed tomographic reconstruction rather than conditional CBCT-to-CT synthesis,.Source: A. Positioning Against Existing Methods · p. 2
  • The method’s raw data consistency directly constrains synthesized CT using the projection measurements from the corresponding acquisition.This is the distinction from EqDiff and EPC-3D-Diff, described here.Source: A. Positioning Against Existing Methods · p. 2

B. Main Contributions

EPC-RawDC integrates two complementary projection constraints with conditional 3D latent diffusion. Its measurement model uses a post-log Gaussian approximation to motivate quadratic projection-domain consistency terms.

B. Main Contributions

  • EPC-RawDC combines geometry-derived projection supervision and scan-specific raw data consistency within a common acquisition forward model for conditional 3D latent diffusion.The two constraints encode complementary reference geometry and individual-acquisition measurements.Source: B. Main Contributions · p. 2
  • Geometry-transformed supervision uses the scanner’s object-rotation and projection-angle-shift relationship, while RawDC uses measurements from the corresponding acquisition.The framework was evaluated on independent datasets with distinct scanner geometries and controlled component ablations.Source: B. Main Contributions · p. 2

A. Statistical CT and CBCT Measurement Model

  • For sufficiently high photon counts, a Gaussian approximation to Poisson statistics and a first-order log approximation support a quadratic projection-domain data fidelity.With uniform weighting, the weighted least-squares objective reduces to standard least squares,.Source: A. Statistical CT and CBCT Measurement… · p. 2

B. CBCT Geometry Induced Projection Equivariance

Circular CBCT geometry links rotations of the attenuation volume to angular shifts in its projections. The framework uses this scanner-derived relation to construct geometry-transformed reference projection supervision.

B. CBCT Geometry Induced Projection Equivariance

  • In circular CBCT, rotating the object about the scanner axis corresponds to an angular displacement of its projections.This relation follows from the rotating source-detector geometry, not from a generic image-augmentation prior.Source: B. CBCT Geometry Induced Projection… · p. 3
  • The relation defines an intertwining between image-domain rotations and projection-domain angular translations, forming the physical basis for geometry-derived projection constraints.It is determined by circular scanner geometry rather than learned from training data.Source: B. CBCT Geometry Induced Projection… · p. 3
  • In discrete implementation, the relation is approximate; angular translation uses an integer shift for sampled angles or fractional interpolation otherwise.Discretization affects projection angles, detector grid, volume, and rotational interpolation.Source: B. CBCT Geometry Induced Projection… · p. 3
  • The operator relation does not itself make the learned synthesis mapping equivariant; it supplies transformed reference targets, distinct from RawDC’s scan-specific measurement targets.Both terms use the same scanner model but constrain predictions with different projection-domain targets.Source: B. CBCT Geometry Induced Projection… · p. 3

III. PROPOSED EPC-RAWDC FRAMEWORK

EPC-RawDC combines conditional 3D latent diffusion with geometry-derived reference projections and scan-specific noisy measurements. The diffusion model operates in a compact volumetric latent space, while physics constraints are evaluated on the decoded image estimate.

III. PROPOSED EPC-RAWDC FRAMEWORK

  • The framework combines conditional 3D latent diffusion with geometry-transformed reference projection supervision and RawDC from the individual scan’s noisy measurements.Both projection terms are built on the acquisition model described in the framework.Source: §III · p. 3
  • The reference CT, aligned CBCT, and scanner-specific forward projector define the framework’s image inputs and acquisition model.The projector operates at the acquisition’s native detector resolution.Source: §III · p. 3

A. Conditional 3D Latent Diffusion Model

  • A shared encoder maps paired CT and CBCT volumes into a compact volumetric latent space for conditional diffusion.The latent representation compresses in-plane dimensions while retaining volumetric depth, lowering memory cost and enabling inter-slice context.Source: A. Conditional 3D Latent Diffusion Model · p. 3
  • A conditional 3D UNet denoises the target CT latent using the noisy latent, diffusion timestep, and CBCT latent condition.The predicted clean latent is decoded to the synthetic CT volume.Source: A. Conditional 3D Latent Diffusion Model · p. 3
  • Physics constraints act on the predicted clean CT image rather than directly on the noisy latent.This lets the acquisition model operate on an image-domain attenuation estimate while the generative prior is learned in latent space.Source: A. Conditional 3D Latent Diffusion Model · p. 3

B. Geometry Derived Equivariance Projection Constraint

The geometry-derived constraint uses the CBCT operator’s rotational symmetry to supervise predictions against transformed reference projections. RawDC complements it with scan-specific supervision from noisy measured projections.

B. Geometry Derived Equivariance Projection Constraint

  • The equivariant loss compares projections of rotated predictions with the corresponding angularly translated reference projections.The rotation is about the CBCT scanner axis, and the reference target is the noise-free projection of the reference CT under the CBCT geometry.Source: B. Geometry Derived Equivariance… · p. 3
  • In discrete implementations, sampling and interpolation make the transformed formulation not exactly equivalent to unrotated projection matching.The ideal continuous circular geometry has zero operator residual; the discrete implementation does not.Source: B. Geometry Derived Equivariance… · p. 4

C. Raw Data Consistency Constraint

  • The RawDC loss is normalized by the number of projection samples, making its magnitude less dependent on view and detector counts.Mc denotes the number of projection samples used in the loss.Source: C. Raw Data Consistency Constraint · p. 4
  • RawDC constrains the predicted CT using the particular scan’s noisy projection measurements rather than a transformed noise-free reference target.Its measurement model approximates post-log data as yc = Acx + nc, with nc ∼ N(0, Σc).Source: C. Raw Data Consistency Constraint · p. 4

D. Overall Training Objective

The training objective combines conditional latent diffusion with image-domain and projection-domain constraints. Projection operators and raw measurements are used for training supervision, while inference conditions on the reconstructed CBCT volume.

D. Overall Training Objective

  • Image-domain regularization is retained to preserve quantitative voxel accuracy and local anatomical structure.The image-domain terms use the 3D finite-difference gradient and Laplacian operators.Source: D. Overall Training Objective · p. 4
  • The complete objective combines conditional latent diffusion, image-domain fidelity losses, geometry-transformed reference projection supervision, and scan-specific RawDC supervision.The terms are intended to act at complementary levels, combining a learned 3D generative prior with scanner-derived geometry and patient-specific measurement information.Source: D. Overall Training Objective · p. 4
  • At inference, only the reconstructed CBCT volume is required; projection operators and raw measurements are used only as training supervision.For a new patient, projection agreement is encouraged by the learned conditional model rather than explicitly enforced.Source: D. Overall Training Objective · p. 5

IV. EXPERIMENTAL DATA AND ACQUISITION GEOMETRY

The study evaluates EPC-RawDC on two independent head-and-neck cohorts with distinct clinical populations and CBCT geometries. It uses simulated projection data for SynthRAD2025 and clinical raw projections for JUST, while retaining the corresponding scanner forward operators.

IV. EXPERIMENTAL DATA AND ACQUISITION GEOMETRY

  • All volumes were resampled to 50 × 256 × 256 voxels at 1 × 1 × 3 mm spacing, and training and testing were separated by patient.Intensities were clipped to [−1000, 2000] HU and linearly mapped to [−1, 1].Source: §IV · p. 5

A. SynthRAD2025 Cohort

  • SynthRAD2025 projection measurements were simulated from reference CT volumes using a Varian cone-beam geometry and Poisson photon statistics.The dataset does not distribute raw projection measurements; the forward operator used ASTRA, with incident fluence I0 = 104 photons per ray.Source: A. SynthRAD2025 Cohort · p. 5

B. JUST Clinical Cohort

  • JUST physics constraints used measured clinical raw CBCT projections from an Elekta acquisition with 220 views and a 512 × 512 detector.Paired CT and CBCT volumes were spatially aligned and resampled to ensure voxelwise correspondence.Source: B. JUST Clinical Cohort · p. 5

V. RESULTS

  • The evaluation covered component contributions, cross-dataset and geometry generalization, joint multi-domain training, and 3D-versus-2D modeling.Metrics were computed per patient; cohort results are reported as mean ± standard deviation, with MAE in HU and SSIM and PSNR computed after normalization.Source: §V · p. 5

A. Implementation Details

EPC-RawDC was evaluated on two patient-separated, single-domain cohorts using consistent scanner-specific settings. Combining geometry-derived and scan-specific projection supervision produced the strongest overall quantitative results in both cohorts.

A. Implementation Details

  • The same network and optimization configuration was used for both cohorts, with dataset- and scanner-specific geometry changed accordingly.The conditional 3D UNet used 64 base channels, diffusion ran for 1000 time steps, and validation used 100-step DDIM sampling.Source: A. Implementation Details · p. 5

B. Single Domain Performance and Component Ablation

  • Single-domain training and testing used the same cohort and CBCT geometry, with patient-level splits and eight JUST and 24 SynthRAD2025 test patients.The split was defined at patient level to prevent information leakage between training and testing.Source: B. Single Domain Performance and… · p. 5
  • SSIM reached 0.97 in both cohorts, with the highest PSNR of 39.18 dB for SynthRAD2025 and 38.00 dB for JUST; EPC-RawDC also reduced mean MAE versus DDPM by 20.3% and 19.0%, respectively.EPC-RawDC had the best overall results in both datasets and higher PSNR and lower MAE than 3D ResUNet and 3D CycleGAN.Source: Table II · p. 6, B. Single Domain Performance and… · pp. 6–7
  • EPC-3D-Diff and RawDC each improved upon DDPM, while their combination produced the best mean performance across both datasets.The geometry-derived reference projection term and scan-specific measurement supervision provide complementary constraints; some incremental differences relative to RawDC were not statistically significant.Source: B. Single Domain Performance and… · pp. 6–7

C. Cross Dataset Generalization under Fixed Geometry

With acquisition geometry held fixed, EPC-RawDC improved over DDPM in both cross-dataset transfer directions. Joint training also improved on DDPM, but domain-specific training performed better when sufficient scanner-specific training data were available.

C. Cross Dataset Generalization under Fixed Geometry

  • 1.32 dB PSNR gain and 23.7% MAE reduction over DDPM accompanied an approximately 5.7% SSIM increase when transferring SynthRAD2025 training to JUST.Relative to RawDC, EPC-RawDC maintained the same SSIM at reported precision, improved PSNR by 0.47 dB, and reduced MAE by approximately 5.6%.Source: Table III · p. 7, C. Cross Dataset Generalization under… · p. 7
  • For JUST-to-SynthRAD2025 transfer, EPC-RawDC increased SSIM by approximately 5.6% and reduced MAE by 6.8% versus DDPM, while PSNR increased by 0.04 dB.The overall trend was the same in both transfer directions, although improvement was smaller in this direction.Source: Table IV · p. 7, C. Cross Dataset Generalization under… · p. 7

D. Joint Multi Domain Training

  • Joint training used both cohorts while retaining each sample's corresponding scanner-specific forward operator, then evaluated the shared model on each held-out test cohort.The model was evaluated independently on the held-out SynthRAD2025 and JUST cohorts.Source: D. Joint Multi Domain Training · p. 7
  • Joint EPC-RawDC training improved over DDPM, increasing PSNR by 0.49 dB on SynthRAD2025 and 0.35 dB on JUST while reducing MAE by 6.5% and 5.8%, respectively.SSIM increased by approximately 1.1% in each cohort.Source: Table V · p. 7, D. Joint Multi Domain Training · p. 7
  • Joint training reduced SSIM by approximately 2.1% in both cohorts and PSNR by 4.61 dB on SynthRAD2025 and 3.46 dB on JUST versus single-domain training, while MAE rose by 81.8% and 69.0%.The paper reports that domain-specific training provides greater structural similarity, contrast fidelity, and voxelwise intensity accuracy when sufficient scanner-specific training data are available.Source: D. Joint Multi Domain Training · pp. 7–8, Table VI · p. 8

E. Volumetric 3D Versus Slice Wise 2D Modeling

Volumetric 3D modeling outperformed slice-wise 2D synthesis, and EPC-RawDC improved on geometry-constrained 3D synthesis. The physics-specific analysis found lower projection and geometry-transformed errors for EPC-RawDC than DDPM.

E. Volumetric 3D Versus Slice Wise 2D Modeling

  • 14.24 dB higher PSNR and approximately 75.1% lower MAE than 2D EqDiff; EPC-RawDC also improved on EPC-3D-Diff and 3D DDPM.The comparison covered all 24 SynthRAD2025 test subjects under the coronal evaluation protocol.Source: E. Volumetric 3D Versus Slice Wise 2D… · p. 8, Table VII · p. 8
  • EPC-RawDC had the closest visual agreement with reference CT and the highest PSNR and SSIM across the displayed examples.The 3D methods preserved more coherent coronal anatomy than 2D approaches, which showed stronger slice-dependent variation and discontinuity.Source: E. Volumetric 3D Versus Slice Wise 2D… · p. 8, Figure 3 · p. 9
  • The reported findings identify volumetric anatomical context as the principal improvement, with RawDC adding gain beyond geometry-derived projection supervision alone.Spatially coherent volumes are described as relevant to registration, contour propagation, and dose-related analysis in radiotherapy.Source: E. Volumetric 3D Versus Slice Wise 2D… · p. 8

F. Physics Specific Consistency Analysis

  • 2.27×10^-3 for DDPM versus 1.02 × 10^-3 for EPC-RawDC in mean projection consistency error, a 55.0% reduction relative to DDPM.EPC-3D-Diff had a mean error of 1.05 × 10^-3; lower values indicate greater agreement with projection data.Source: F. Physics Specific Consistency Analysis · p. 8, Table VIII · p. 8
  • 41.4% lower geometry-transformed projection error than DDPM and 18.9% lower than EPC-3D-Diff for EPC-RawDC.The geometry metric measures agreement with transformed reference projections, not direct equivariance of the learned synthesis mapping.Source: F. Physics Specific Consistency Analysis · pp. 8–9

G. Patient Level Statistical Analysis

Patient-level comparisons found EPC-RawDC consistently outperformed DDPM across both cohorts, although significance against alternatives varied by metric and cohort. The conclusion reports lower mean MAE than DDPM across cohorts and identifies broader validation and downstream radiotherapy evaluation as future work.

G. Patient Level Statistical Analysis

  • EPC-RawDC outperformed DDPM in all 24 SynthRAD2025 patients for SSIM, PSNR, and MAE, with all comparisons significant after correction (padj < 0.001).Against EPC-3D-Diff, all three metrics were significant; against RawDC, only SSIM was significant.Source: G. Patient Level Statistical Analysis · p. 10
  • In JUST, EPC-RawDC outperformed DDPM in all 8 patients for all three metrics; corrected improvements were significant for SSIM (padj < 0.001) and MAE (padj = 0.002), but not PSNR (padj = 0.073).Against EPC-3D-Diff and RawDC, SSIM and MAE differences were significant, while PSNR differences were not.Source: G. Patient Level Statistical Analysis · p. 10
  • Across subjects, improvement over DDPM was highly consistent, while incremental gains over EPC-3D-Diff and RawDC were most evident in SSIM and, for JUST, MAE.The patient-level comparisons used matched measurements and corrected nine prespecified comparisons per cohort.Source: G. Patient Level Statistical Analysis · pp. 9–10

VI. CONCLUSION

  • Mean MAE relative to DDPM fell by 20.3% on SynthRAD2025 and 19.0% on JUST; the conclusion identifies broader multicenter validation and downstream radiotherapy-task evaluation as future work.The proposed downstream work includes dose calculation and adaptive treatment workflows.Source: §VI · p. 10
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