EPC-3D-Diff: Equivariant Physics Consistent Conditional 3D Latent Diffusion for CBCT to CT Synthesis

Ahmad Qendel; Alessandro Perelli; Alzahra Altalib; Chunhui Li; Haytham Al Ewaidat; Khaled Alawneh

arxiv: 2605.20470 · v1 · pith:ZGZ4XQJZnew · submitted 2026-05-19 · 💻 cs.CV · cs.AI· physics.med-ph

EPC-3D-Diff: Equivariant Physics Consistent Conditional 3D Latent Diffusion for CBCT to CT Synthesis

Alzahra Altalib , Chunhui Li , Haytham Al Ewaidat , Khaled Alawneh , Ahmad Qendel , Alessandro Perelli This is my paper

Pith reviewed 2026-05-21 06:29 UTC · model grok-4.3

classification 💻 cs.CV cs.AIphysics.med-ph

keywords CBCT to CT synthesislatent diffusionequivariance lossprojection domainradiotherapyHounsfield unitsphysics consistent3D autoencoder

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The pith

A projection-domain equivariance loss in latent diffusion produces more accurate and physics-consistent CBCT-to-CT synthesis.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents EPC-3D-Diff, a conditional 3D diffusion model that converts cone-beam CT scans into higher-quality CT volumes for radiotherapy use. It adds a loss term that exploits the physical fact that rotating a volume should produce an angular shift in its X-ray projections. Training enforces this by forward-projecting rotated synthesized volumes and matching the results to shifted projections from the paired target CT. The diffusion process runs in a compact latent space produced by a 3D autoencoder so full volumetric context remains tractable. On both phantom and clinical paired datasets the approach raises PSNR, SSIM, and Hounsfield-unit fidelity inside tissue boundaries relative to prior diffusion and CycleGAN methods.

Core claim

By embedding a projection-domain equivariance constraint that links volume rotations to angular projection shifts directly into the diffusion training objective, EPC-3D-Diff achieves higher quantitative accuracy and physical consistency in CBCT-to-CT synthesis than standard image-domain or unpaired baselines.

What carries the argument

The projection-domain equivariance loss that matches forward projections of rotated synthesized CT volumes against angle-shifted projections of the paired target CT.

If this is right

Synthesized volumes exhibit higher PSNR, SSIM, and Hounsfield-unit accuracy within tissue boundaries on both phantom and patient data.
The model supports single-domain and mixed-domain training while preserving generalization across repeat scans.
Physics consistency improves robustness against typical CBCT artifacts such as scatter and noise.
The resulting images become more suitable for quantitative radiotherapy planning and dose calculation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same rotation-to-shift principle could be extended to other known geometric transforms such as translations to strengthen consistency further.
Replacing the simple forward projector with a more complete simulator that includes scatter might reduce sensitivity to real calibration mismatches.
Because the method operates in latent space, inference speed could be increased enough for online adaptive radiotherapy workflows.

Load-bearing premise

The paired CBCT and CT datasets faithfully capture the true physical relationship between volumes and projections, and the forward projector used for the loss accurately models scanner geometry without unaccounted scatter or calibration errors.

What would settle it

Measure whether the reported PSNR and HU gains remain when the same model is tested on CBCT volumes acquired on a scanner with different geometry or with deliberately introduced scatter.

Figures

Figures reproduced from arXiv: 2605.20470 by Ahmad Qendel, Alessandro Perelli, Alzahra Altalib, Chunhui Li, Haytham Al Ewaidat, Khaled Alawneh.

**Figure 2.** Figure 2: Qualitative testing comparison on NWH phantom test set. Columns show [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Qualitative testing comparison on JUST clinical test set. Columns show [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Quantitative analysis on JUST clinical test set. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

read the original abstract

Cone-beam CT (CBCT) is routinely acquired during radiotherapy for patient setup, but its quantitative reliability is degraded by scatter, noise, and reconstruction artifacts, limiting Hounsfield Unit (HU) accuracy. We propose EPC-3D-Diff, a novel conditional 3D latent diffusion framework for volumetric CBCT to CT synthesis that introduces a projection domain equivariance loss derived from acquisition physics. Unlike common image domain equivariance, we exploit the fact that an in plane rotation of the volume corresponds to an angular shift in its projections. During training, we enforce this relationship by forward projecting rotated synthesized CT volumes and matching them to appropriately angle shifted projections of the paired target CT, yielding a physics consistent equivariance constraint integrated into the diffusion objective. To capture full 3D context efficiently, conditional diffusion is performed in a compact latent space learnt by a lightweight 3D autoencoder, preserving axial depth while downsampling in plane resolution for stable training. We validate on a paired head CBCT/CT phantom dataset, including repeat scans, and paired clinical data using patient wise splits, and perform single and mixed domain training, ablations, and comparisons with diffusion and CycleGAN. EPC-3D-Diff generalizes well and achieved substantial improvements, +7.4 dB (phantom) and +1.8 dB (clinical data) in PSNR compared to state of the art methods, alongside improved SSIM and HU accuracy, within tissue boundaries. Overall, EPC-3D-Diff improves robustness and physics consistency, supporting HU aware synthesis for downstream radiotherapy workflows.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The projection-domain equivariance loss is the main technical addition, and the reported PSNR gains look real on the data they tested, but the paper needs clearer ablations to show the loss is doing the heavy lifting.

read the letter

The main thing to know is that EPC-3D-Diff combines a 3D latent diffusion model with a projection-domain equivariance loss that turns volume rotations into angular projection shifts. This gives a physics-based constraint during training by forward-projecting the synthesized CT and matching it to shifted target projections. They run it on paired phantom and clinical head data with patient-wise splits and beat diffusion and CycleGAN baselines by 7.4 dB PSNR on phantom and 1.8 dB on clinical, plus better SSIM and HU values inside tissue boundaries. The latent-space diffusion keeps the 3D context manageable without blowing up compute. That combination of conditional diffusion plus the geometry-derived loss is the actual new piece. It is not just another image-domain equivariance trick. The setup is straightforward and the results are reported on both repeat phantom scans and real patient data, which is better than many synthesis papers that stay on phantoms only. The forward projection is derived from known CBCT geometry rather than learned from intensities, so the constraint has some independent grounding. The soft spots are mostly in the evidence. The abstract mentions ablations and single versus mixed domain training but does not show the numbers or error bars, so it is hard to judge how much the equivariance term actually moves the needle versus the diffusion backbone alone. There are also no statistical tests on the HU improvements. The forward projector itself is described at a high level; if it is a basic ray-tracing model it will miss scatter, beam hardening, and calibration drift that exist in real scanners. That could mean the physics consistency claim is weaker than it appears on clinical data. This paper is for people working on quantitative CBCT correction for radiotherapy planning. A reader who cares about physics-informed generative models will find the loss construction useful even if they adapt it. It is solid enough on the core idea and the reported gains to deserve a serious referee rather than a desk reject. I would send it out for review with a request for the missing ablation tables and a clearer description of the projector.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes EPC-3D-Diff, a conditional 3D latent diffusion framework for CBCT to CT synthesis. It introduces a projection-domain equivariance loss derived from CBCT acquisition physics, exploiting that an in-plane volume rotation corresponds to an angular shift in projections. During training, rotated synthesized CT volumes are forward-projected and matched to angle-shifted projections of the paired target CT. Diffusion occurs in a compact latent space from a lightweight 3D autoencoder. Validation uses paired head phantom (with repeat scans) and clinical data under patient-wise splits, with single/mixed domain training, ablations, and comparisons to diffusion and CycleGAN baselines. The paper reports PSNR gains of +7.4 dB (phantom) and +1.8 dB (clinical), plus improved SSIM and HU accuracy within tissue boundaries.

Significance. If substantiated, the work could meaningfully improve quantitative reliability of CBCT for radiotherapy workflows by adding an independent physics-based constraint to a latent diffusion model. The equivariance construction supplies grounding separate from the data-driven objective, and the latent-space design supports efficient full-3D context. The reported gains and patient-wise evaluation setup are relevant to clinical translation.

major comments (2)

[Abstract and Methods (equivariance loss)] Abstract and Methods (equivariance loss): The loss is implemented by forward-projecting rotated synthesized CT volumes and matching to angle-shifted projections of the paired target CT. No explicit description is given of how the forward projection operator incorporates or corrects for real CBCT effects such as scatter, beam hardening, noise, or geometric calibration deviations. If the operator is a simplified ray-tracing model, the enforced relationship may not correspond to actual scanner physics, weakening the causal attribution of HU accuracy gains to the physics constraint rather than the diffusion backbone alone.
[Results and Evaluation] Results and Evaluation: The abstract states PSNR/SSIM/HU improvements and mentions ablations, but provides no detailed ablation results on the equivariance loss weight, error bars, or statistical tests. This leaves only moderate support for the central claim that the equivariance term drives the reported +7.4 dB (phantom) and +1.8 dB (clinical) gains and improved tissue-boundary accuracy.

minor comments (2)

[Abstract] The claim that the method 'generalizes well' would be strengthened by explicit quantitative comparison of single-domain versus mixed-domain training outcomes.
[Results] Ensure all quantitative tables and figures include error bars and clear statistical annotations to support reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive comments on our manuscript. We address each of the major comments below and have made revisions to the manuscript to incorporate the feedback where possible.

read point-by-point responses

Referee: Abstract and Methods (equivariance loss): The loss is implemented by forward-projecting rotated synthesized CT volumes and matching to angle-shifted projections of the paired target CT. No explicit description is given of how the forward projection operator incorporates or corrects for real CBCT effects such as scatter, beam hardening, noise, or geometric calibration deviations. If the operator is a simplified ray-tracing model, the enforced relationship may not correspond to actual scanner physics, weakening the causal attribution of HU accuracy gains to the physics constraint rather than the diffusion backbone alone.

Authors: We are grateful to the referee for pointing out the need for greater clarity on the forward projection operator. Our implementation employs a ray-tracing forward projector that faithfully represents the CBCT scanner's geometric configuration, such as the source-to-isocenter and source-to-detector distances, as well as the angular increments. This geometric modeling ensures that the equivariance constraint aligns with the physical acquisition process for rotational transformations. We concur that the operator does not include explicit corrections for scatter, beam hardening, or noise, which are often mitigated by manufacturer-specific preprocessing in clinical practice. The equivariance loss is designed to promote physics consistency at the geometric level, which is a significant factor in CBCT artifacts. In the revised manuscript, we have included an expanded description of the projection operator in the Methods section, along with a discussion of its assumptions and limitations. This should better substantiate the contribution of the physics constraint. revision: partial
Referee: Results and Evaluation: The abstract states PSNR/SSIM/HU improvements and mentions ablations, but provides no detailed ablation results on the equivariance loss weight, error bars, or statistical tests. This leaves only moderate support for the central claim that the equivariance term drives the reported +7.4 dB (phantom) and +1.8 dB (clinical) gains and improved tissue-boundary accuracy.

Authors: Thank you for this observation regarding the results presentation. The original manuscript does include ablation experiments demonstrating the impact of the equivariance loss by comparing variants with and without it. To provide stronger evidence, we have revised the Results section to include detailed ablation studies on the loss weight hyperparameter, reporting performance metrics for a range of weights. Additionally, we now report error bars based on multiple training runs with different random seeds and include statistical tests (e.g., paired t-tests) to assess the significance of improvements. These updates offer more robust support for the claim that the equivariance term contributes to the observed gains in PSNR, SSIM, and HU accuracy. revision: yes

Circularity Check

0 steps flagged

No significant circularity; physics-derived equivariance constraint is independent of fitted outputs.

full rationale

The paper's central derivation introduces a projection-domain equivariance loss based on the known CBCT acquisition geometry: an in-plane rotation of the volume corresponds to an angular shift in projections. This is enforced by forward-projecting rotated synthesized CT volumes and matching them to angle-shifted projections of the paired target CT, then integrating the resulting constraint into the diffusion objective. This step relies on external physics of the scanner geometry rather than being defined in terms of the synthesized intensities, the diffusion predictions, or any fitted parameters from the target data. No self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations appear in the abstract or described chain. The reported PSNR/SSIM/HU gains are presented as outcomes of the combined latent diffusion plus independent physics constraint, keeping the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The approach rests on standard diffusion training and autoencoder compression plus one key physics relationship; hyperparameters for loss balancing and latent dimensions are not detailed in the abstract.

free parameters (2)

Equivariance loss weight
Balancing coefficient between the diffusion objective and the projection equivariance term is a tunable hyperparameter.
Latent space resolution
Downsampling factors and channel dimensions in the 3D autoencoder are architectural choices that affect training stability and reconstruction fidelity.

axioms (1)

domain assumption An in-plane rotation of the volume corresponds to an angular shift in its projections
This relationship is used to construct the equivariance loss by forward-projecting rotated synthesized volumes and matching them to angle-shifted target projections.

pith-pipeline@v0.9.0 · 5851 in / 1427 out tokens · 62740 ms · 2026-05-21T06:29:32.816354+00:00 · methodology

discussion (0)

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ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

an in plane rotation of the volume corresponds to an angular shift in its projections... Leq = sum ||T_ϕi(y0) - A0 R_ϕi(ˆx0)||²₂

What do these tags mean?

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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

[1]

arXiv preprint arXiv:2509.17790 (2025)

Altalib, A., Li, C., Perelli, A.: Conditional diffusion models for CT image synthesis from CBCT: A systematic review. arXiv preprint arXiv:2509.17790 (2025)

work page arXiv 2025
[2]

IEEE Transactions on Radiation and Plasma Medical Sciences9(6), 691–707 (2025)

Altalib, A., McGregor, S., Li, C., Perelli, A.: Synthetic CT image generation from CBCT: a systematic review. IEEE Transactions on Radiation and Plasma Medical Sciences9(6), 691–707 (2025)

work page 2025
[3]

IEEE Access8, 225981–225994 (2020)

Bayaraa, T., Hyun, C.M., Jang, T.J., Lee, S.M., Seo, J.K.: A two-stage approach for beam hardening artifact reduction in low-dose dental CBCT. IEEE Access8, 225981–225994 (2020)

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In: Proceedings of the IEEE/CVF International Conference on Com- puter Vision

Chen, D., Tachella, J., Davies, M.E.: Equivariant imaging: Learning beyond the range space. In: Proceedings of the IEEE/CVF International Conference on Com- puter Vision. pp. 4379–4388 (2021)

work page 2021
[5]

Medical physics47(3), 1115–1125 (2020)

Chen, L., Liang, X., Shen, C., Jiang, S., Wang, J.: Synthetic CT generation from CBCT images via deep learning. Medical physics47(3), 1115–1125 (2020)

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Medical physics51(11), 8168–8178 (2024)

Chen, X., Qiu, R.L., Peng, J., Shelton, J.W., Chang, C.W., Yang, X., Kesarwala, A.H.: CBCT-based synthetic CT image generation using a diffusion model for CBCT-guided lung radiotherapy. Medical physics51(11), 8168–8178 (2024)

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Advances in neural information processing systems33, 6840–6851 (2020)

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Physics in Medicine and Biology64(12), 125002 (2019)

Liang, X., Chen, L., Nguyen, D., Zhou, Z., Gu, X., Yang, M., Wang, J., Jiang, S.: Generating synthesized computed tomography (CT) from cone-beam computed tomography (CBCT) using CycleGAN for adaptive radiation therapy. Physics in Medicine and Biology64(12), 125002 (2019)

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Medical physics51(3), 1847–1859 (2024) 10 Alzahra Altalib et al

Peng, J., Qiu, R.L., Wynne, J.F., Chang, C.W., Pan, S., Wang, T., Roper, J., Liu, T., Patel, P.R., Yu, D.S., et al.: CBCT-based synthetic CT image generation using conditional denoising diffusion probabilistic model. Medical physics51(3), 1847–1859 (2024) 10 Alzahra Altalib et al

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Medical physics48(11), 6537–6566 (2021)

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Yang, T.J., Wen, P.P., Ye, X., Wu, X.F., Zhang, C., Sun, S.Y., Wu, Z.X., Zhang, G.Y., Sun, Y.F., Ye, R., et al.: CT Hounsfield units in assessing bone and soft tissue quality in the proximal femur: a systematic review focusing on osteonecrosis and total hip arthroplasty. Plos one20(3), e0319907 (2025)

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Med- ical Physics52(11), e70126 (2025)

Yeap, P.L., Du, X., Zhou, M., Hoole, A., Barnett, G.C., Jena, R.: Few-shot CBCT- based synthetic CT generation with denoising diffusion probabilistic model. Med- ical Physics52(11), e70126 (2025)

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[1] [1]

arXiv preprint arXiv:2509.17790 (2025)

Altalib, A., Li, C., Perelli, A.: Conditional diffusion models for CT image synthesis from CBCT: A systematic review. arXiv preprint arXiv:2509.17790 (2025)

work page arXiv 2025

[2] [2]

IEEE Transactions on Radiation and Plasma Medical Sciences9(6), 691–707 (2025)

Altalib, A., McGregor, S., Li, C., Perelli, A.: Synthetic CT image generation from CBCT: a systematic review. IEEE Transactions on Radiation and Plasma Medical Sciences9(6), 691–707 (2025)

work page 2025

[3] [3]

IEEE Access8, 225981–225994 (2020)

Bayaraa, T., Hyun, C.M., Jang, T.J., Lee, S.M., Seo, J.K.: A two-stage approach for beam hardening artifact reduction in low-dose dental CBCT. IEEE Access8, 225981–225994 (2020)

work page 2020

[4] [4]

In: Proceedings of the IEEE/CVF International Conference on Com- puter Vision

Chen, D., Tachella, J., Davies, M.E.: Equivariant imaging: Learning beyond the range space. In: Proceedings of the IEEE/CVF International Conference on Com- puter Vision. pp. 4379–4388 (2021)

work page 2021

[5] [5]

Medical physics47(3), 1115–1125 (2020)

Chen, L., Liang, X., Shen, C., Jiang, S., Wang, J.: Synthetic CT generation from CBCT images via deep learning. Medical physics47(3), 1115–1125 (2020)

work page 2020

[6] [6]

Medical physics51(11), 8168–8178 (2024)

Chen, X., Qiu, R.L., Peng, J., Shelton, J.W., Chang, C.W., Yang, X., Kesarwala, A.H.: CBCT-based synthetic CT image generation using a diffusion model for CBCT-guided lung radiotherapy. Medical physics51(11), 8168–8178 (2024)

work page 2024

[7] [7]

Handbook of medical imaging2, 1–70 (2000)

Fessler, J.A., Sonka, M., Fitzpatrick, J.M.: Statistical image reconstruction meth- ods for transmission tomography. Handbook of medical imaging2, 1–70 (2000)

work page 2000

[8] [8]

Computerized Medical Imaging and Graphics113, 102344 (2024)

Fu, L., Li, X., Cai, X., Miao, D., Yao, Y., Shen, Y.: Energy-guided diffusion model for CBCT-to-CT synthesis. Computerized Medical Imaging and Graphics113, 102344 (2024)

work page 2024

[9] [9]

Advances in neural information processing systems33, 6840–6851 (2020)

Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Advances in neural information processing systems33, 6840–6851 (2020)

work page 2020

[10] [10]

Cyber Security| Big Data| AI

Kitson, S.L.: Modern medical imaging and radiation therapy. Cyber Security| Big Data| AI. Open Med Science (2024)

work page 2024

[11] [11]

Physics in Medicine and Biology64(12), 125002 (2019)

Liang, X., Chen, L., Nguyen, D., Zhou, Z., Gu, X., Yang, M., Wang, J., Jiang, S.: Generating synthesized computed tomography (CT) from cone-beam computed tomography (CBCT) using CycleGAN for adaptive radiation therapy. Physics in Medicine and Biology64(12), 125002 (2019)

work page 2019

[12] [12]

Medical physics51(3), 1847–1859 (2024) 10 Alzahra Altalib et al

Peng, J., Qiu, R.L., Wynne, J.F., Chang, C.W., Pan, S., Wang, T., Roper, J., Liu, T., Patel, P.R., Yu, D.S., et al.: CBCT-based synthetic CT image generation using conditional denoising diffusion probabilistic model. Medical physics51(3), 1847–1859 (2024) 10 Alzahra Altalib et al

work page 2024

[13] [13]

Medical Physics49(9), 6019–6054 (2022)

Rusanov,B.,Hassan,G.M.,Reynolds,M.,Sabet,M.,Kendrick,J.,Rowshanfarzad, P., Ebert, M.: Deep learning methods for enhancing cone-beam CT image quality toward adaptive radiation therapy: A systematic review. Medical Physics49(9), 6019–6054 (2022)

work page 2022

[14] [14]

Medical physics48(11), 6537–6566 (2021)

Spadea, M.F., Maspero, M., Zaffino, P., Seco, J.: Deep learning based synthetic-CT generation in radiotherapy and PET: a review. Medical physics48(11), 6537–6566 (2021)

work page 2021

[15] [15]

Plos one20(3), e0319907 (2025)

Yang, T.J., Wen, P.P., Ye, X., Wu, X.F., Zhang, C., Sun, S.Y., Wu, Z.X., Zhang, G.Y., Sun, Y.F., Ye, R., et al.: CT Hounsfield units in assessing bone and soft tissue quality in the proximal femur: a systematic review focusing on osteonecrosis and total hip arthroplasty. Plos one20(3), e0319907 (2025)

work page 2025

[16] [16]

Med- ical Physics52(11), e70126 (2025)

Yeap, P.L., Du, X., Zhou, M., Hoole, A., Barnett, G.C., Jena, R.: Few-shot CBCT- based synthetic CT generation with denoising diffusion probabilistic model. Med- ical Physics52(11), e70126 (2025)

work page 2025