Inferring　the　complete　traffic　flow　time–space　diagram　using　vehicle　trajectories　provides　a　holistic　perspective　of　traffic　dynamics　at　intersections　to　traffic　managers.　However,　obtaining　all　vehicle　trajectories　on　the　road　is　infeasible.　To　this　end,　a　novel　framework　that　combines　the　conditional　deep　generative　model　and　physics-based　car-following　model　is　proposed　to　reconstruct　all　vehicle　trajectories　from　sparsely　available　connected　vehicle　(CV)　trajectories　at　the　intersection.　The　proposed　framework　has　two　novel　components:　Arrival　Generative　Adversarial　Network　(Arrival-GAN)　and　Trajectory-GAN.　The　Arrival-GAN　reproduces　stochastic　vehicle　arrival　patterns　by　considering　the　interaction　between　adjacent　intersections　(e.g.,　signal　control　scheme)　and　the　interaction　between　multiple　vehicles　from　historical　vehicle　trajectories,　circumventing　the　conventionally　adopted　unrealistic　assumptions　of　uniform　vehicle　arrivals.　The　Trajectory-GAN　model　takes　the　baseline　trajectory　deduced　by　the　physics-based　car-following　model　as　prior　information　and　refines　it　by　dynamically　adapting　driving　behavior　in　response　to　the　varying　traffic　conditions　in　a　data-driven　manner.　This　hybrid　approach　leverages　the　advantages　of　data-driven　(i.e.,　flexibility)　and　theory-driven　approaches　(i.e.,　interpretability)　complementarily.　The　proposed　framework　outperforms　conventional　benchmark　models　in　the　simulated　arterial　network　and　the　real-world　datasets,　reconstructing　a　complete　time–space　diagram　at　intersections　with　markedly　enhanced　accuracy,　particularly　in　low-traffic-density　scenarios.　This　study　showcases　the　potential　of　utilizing　CV　data　and　physics-informed　deep　learning　to　improve　our　understanding　of　traffic　dynamics,　empowering　traffic　managers　with　novel　insights　for　efficient　intersection　management.　©　2024　Elsevier　Ltd