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As a result, the assumptions of symmetry and fixed tail weight in Gaussian processes have become restrictive and may fail to capture the intrinsic properties of the data. To address the limitations of the Gaussian models, a variety of skewed models has been proposed, of which the popularity has grown rapidly. These skewed models introduce parameters that govern skewness and tail weight. Among various proposals in the literature, unified skewed distributions, such as the Unified Skew-Normal (SUN), have received considerable attention. In this work, we revisit a more concise and intepretable re-parameterization of the SUN distribution and apply the distribution to random fields by constructing a generalized unified skew-normal (GSUN) spatial process. We demonstrate that the GSUN is a valid spatial process by showing its vanishing correlation at large distances and provide the corresponding spatial interpolation method. In addition, we develop an inference mechanism for the GSUN process using the concept of neural Bayes estimators with deep graphical attention networks (GATs) and encoder transformer. We show the superiority of our proposed estimator over conventional CNN-based architectures in terms of stability and accuracy by means of a simulation study. In addition, we demonstrate that the GSUN process offers enhanced flexibility compared to another model proposed in the literature through an application to Pb-contaminated soil data. Furthermore, we show that the GSUN process is different from the conventional Gaussian processes and Tukey\n                    <jats:italic>g<\/jats:italic>\n                    -and-\n                    <jats:italic>h<\/jats:italic>\n                    processes, through the probability integral transform (PIT).\n                  <\/jats:p>","DOI":"10.1007\/s11222-025-10801-9","type":"journal-article","created":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T03:56:20Z","timestamp":1768708580000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Generalized Unified Skew-Normal Process with Neural Bayes Inference"],"prefix":"10.1007","volume":"36","author":[{"given":"Kesen","family":"Wang","sequence":"first","affiliation":[]},{"given":"Marc G.","family":"Genton","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,1,18]]},"reference":[{"issue":"12","key":"10801_CR1","doi-asserted-by":"publisher","first-page":"2771","DOI":"10.1109\/TPDS.2018.2850749","volume":"29","author":"S Abdulah","year":"2018","unstructured":"Abdulah, S., Ltaief, H., Sun, Y., Genton, M.G., Keyes, D.E.: ExaGeoStat: a high performance unified software for geostatistics on manycore systems. 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