Conditional Image Diffusion with Interferometric Closure Invariants: Independent EHT Imaging of Centaurus~A and 3C~279

Abstract

We present independent imaging analyses of Event Horizon Telescope (EHT) observations of the active galactic nuclei in radio galaxy Centaurus~A and quasar 3C~279 using Generative Deep learning Image Reconstruction with Closure Terms (GenDIReCT), a recently developed machine-learning framework built on conditional diffusion models that uses interferometric closure invariants as primary observables. For Centaurus~A, our reconstruction reveals two prominent emission ridges ($\simeq 80\,μ$as each) along the jet sheath with a brightness ratio of $1.4\pm 0.1$ and an opening angle of $12.3\pm 0.3$~deg. For 3C~279, we identify three distinct components in the image, with the southern jet ejecta on sub-parsec scale exhibiting a proper motion of $4.6\pm 1.0\,μ$as over $\approx 5.39$ days away from the northern components, corresponding to an apparent superluminal velocity of $\simeq 10\pm 2$ times light speed. These measurements are consistent with those reported by the EHT Collaboration. The results are significant because we demonstrate that: (1) imaging from interferometric aperture synthesis data, especially in VLBI and most acutely in extremely sparse arrays like the EHT, remains a severely ill-posed and challenging inverse problem, yet closure invariants preserve robust morphological information that can strongly constrain structural features, and (2) more importantly, closure-invariant imaging largely avoids calibration systematics, thus providing a fundamentally independent view of spatial structure with very high angular resolution. The generative nature of GenDIReCT further allows us to sample and characterise clusters of plausible image solutions for each dataset. As a calibration-independent, generative imaging approach, GenDIReCT offers a robust and truly independent blind-imaging tool for current and future VLBI experiments.

Figures (10)

• Figure 1: Overview of the GenDIReCT architecture, imaging sequence, and outputs. For a single reconstruction, the GenDIReCT model receives a dataset of closure invariants, which can also be derived from synthetic observation of a ground truth image. The pretrained conditional diffusion component samples images decoded from a distribution in the latent feature space, conditioned on the provided data. Subsequently, the convolutional neural network processes the diffusion sample and optimises for consistency with the input closure invariants, resulting in the final image reconstruction.
• Figure 2: Comparison between the EHTC reference reconstructions of blazar 3C 279 (top) and Centaurus A (bottom) with their corresponding GenDIReCT reconstructions. The dataset used in the reconstruction of 3C 279 is from 11 April 2017. GenDIReCT outputs include the best single reconstruction as measured by the reduced $\chi^2_{\rm{CI}}$, the median reconstruction, the median absolute deviation, and ratio images. The ratio image displays the median image over the median absolute deviation, illustrating reconstruction confidence. The synthesised beam is visualised in the left panel with an elliptical model. All 3C 279 reconstructions are plotted on a $225\times225\,\mu{\rm as}^2$ field-of-view, while Centaurus A reconstructions are pictured on a $450\times450\,\mu{\rm as}^2$ field-of-view. All GenDIReCT reconstructions (and the EHTC Centaurus A reference image) are presented without clean beam convolution, while the EHTC reference for 3C 279 has previously been convolved with a $20\,\mu$as circular beam.
• Figure 3: Reconstruction clusters for the EHT observations of 3C 279 (top row) and Centaurus A (bottom row). Each cluster is represented by the median image and we show the percentage share alongside the minimum $\chi^2_{\rm{CI}}$ (in parenthesis) of all reconstructions identified with that cluster. The first image of each row shows the linear scale and fitted clean beam.
• Figure 4: Illustration of the three elliptical Gaussian component fits of both the EHTC reference (left) and median GenDIReCT (right) reconstruction on the 11 April 2017 dataset of 3C 279. The centroid of each component is marked with an 'x' and a single contour is drawn at the half-amplitude.
• Figure 5: Illustration of the EHTC reference (top-left) and median GenDIReCT (top-right) reconstructions fitted with straight lines for each of the northern and southern edge-brightened jet ridgelines. The surface brightness along the fitted ridgeline is represented by the distribution plotted orthogonally to each line. In the bottom row, we compare the northern and southern surface brightness profiles between the EHTC (solid line) and GenDIReCT (dotted line) reconstructions. The bottom-right panel compares the profiles for both reconstructions after convolving with a common $20\,\mu$as circular beam, which is illustrated on the GenDIReCT median image.