BCDDM: Branch-Corrected Denoising Diffusion Model for Black Hole Image Generation

TL;DR

The paper presents BCDDM, a diffusion-based framework for generating black hole images conditioned on seven RIAF parameters to address the high computational cost of GRRT. It introduces a Branch-Corrected U-Net and a mixed loss to enforce both high-fidelity denoising and faithful parameter mapping, enabling dataset augmentation and improved parameter regression. A 2,157-image GRRT dataset is used, with normalization and a 1000-step diffusion schedule, achieving strong image-parameter consistency and enabling ResNet50-based regression improvements when augmenting with synthetic data. The results demonstrate high image fidelity (via SSIM) and enhanced parameter estimation (via $R^2$) when using mixed datasets, suggesting practical utility for faster BH image generation and model fitting in EHT analyses. The approach offers a path toward efficient data augmentation and improved inference, with potential extensions to polarization and more comprehensive accretion disk models.

Abstract

The properties of black holes and accretion flows can be inferred by fitting Event Horizon Telescope (EHT) data to simulated images generated through general relativistic ray tracing (GRRT). However, due to the computationally intensive nature of GRRT, the efficiency of generating specific radiation flux images needs to be improved. This paper introduces the Branch Correction Denoising Diffusion Model (BCDDM), a deep learning framework that synthesizes black hole images directly from physical parameters. The model incorporates a branch correction mechanism and a weighted mixed loss function to enhance accuracy and stability. We have constructed a dataset of 2,157 GRRT-simulated images for training the BCDDM, which spans seven key physical parameters of the radiatively inefficient accretion flow (RIAF) model. Our experiments show a strong correlation between the generated images and their physical parameters. By enhancing the GRRT dataset with BCDDM-generated images and using ResNet50 for parameter regression, we achieve significant improvements in parameter prediction performance. BCDDM offers a novel approach to reducing the computational costs of black hole image generation, providing a faster and more efficient pathway for dataset augmentation, parameter estimation, and model fitting.

Figures (10)

• Figure 1: The diffusion process of black hole images. We output the image every $100$ steps for a total of $1000$ times to observe the changes in the diffusion process of the image.
• Figure 2: BCDDM architecture for black hole image generation. The diffusion process and denoising process utilize the same U-Net model, with detailed architecture illustrated in Figure \ref{['fig-2']}.
• Figure 3: Encoding and Decoding architecture embedded in BCDDM. The trainable components consist solely of the input encoded label vector and black hole image, along with the output predicted parameters and noise.
• Figure 4: Training loss and validation loss during the training process. The right panel displays two independent black hole images generated by BCDDM at epochs $100$, $1000$, $2500$, and $5000$, illustrating the performance progression of the generative model.
• Figure 5: Comparison of original and reconstructed black hole images in the additional test set. The figure presents six pairs of GRRT-simulated original black hole images (top row) alongside their BCDDM-reconstructed counterparts (bottom row). The parameters displayed above the original images represent the ground truth values used as initial inputs, while those below the reconstructed images show the output from the parameter corrector branch. Each reconstructed image is annotated with its NRMSE (Normalized Root Mean Square Error) and SSIM (Structural Similarity index) values compared to the original. All images are rendered in brightness temperature units ($10^{10}K$), calculated as $T = S\lambda^2/(2k_B\Omega)$, where $S$ denotes flux density, $\lambda$ the observation wavelength, $k_B$ the Boltzmann constant, and $\Omega$ the solid angle of the resolution element.