Purpose: To develop and evaluate a deep learning (DL) method for free-breathing phase-sensitive inversion recovery (PSIR) late gadolinium enhancement (LGE) cardiac MRI that produces diagnostic-quality images from a single acquisition over two heartbeats, eliminating the need for 8 to 24 motion-corrected (MOCO) signal averages. Materials and Methods: Raw data comprising 800,653 slices from 55,917 patients, acquired on 1.5T and 3T scanners across multiple sites from 2016 to 2024, were used in this retrospective study. Data were split by patient: 640,000 slices (42,822 patients) for training and the remainder for validation and testing, without overlap. The training and testing data were from different institutions. PSIRNet, a physics-guided DL network with 845 million parameters, was trained end-to-end to reconstruct PSIR images with surface coil correction from a single interleaved IR/PD acquisition over two heartbeats. Reconstruction quality was evaluated using SSIM, PSNR, and NRMSE against MOCO PSIR references. Two expert cardiologists performed an independent qualitative assessment, scoring image quality on a 5-point Likert scale across bright blood, dark blood, and wideband LGE variants. Paired superiority and equivalence (margin = 0.25 Likert points) were tested using exact Wilcoxon signed-rank tests at a significance level of 0.05 using R version 4.5.2. Results: Both readers rated single-average PSIRNet reconstructions superior to MOCO PSIR for dark blood LGE (conservative P = .002); for bright blood and wideband, one reader rated it superior and the other confirmed equivalence (all P < .001). Inference required approximately 100 msec per slice versus more than 5 sec for MOCO PSIR. Conclusion: PSIRNet produces diagnostic-quality free-breathing PSIR LGE images from a single acquisition, enabling 8- to 24-fold reduction in acquisition time.