Driven by human ingenuity and creativity, the discovery of super-resolution techniques, which circumvent the classical diffraction limit of light, represent a leap in optical microscopy. However, the vast space encompassing all possible experimental configurations suggests that some powerful concepts and techniques might have not been discovered yet, and might never be with a human-driven direct design approach. Thus, AI-based exploration techniques could provide enormous benefit, by exploring this space in a fast, unbiased way. We introduce XLuminA, an open-source computational framework developed using JAX, which offers enhanced computational speed enabled by its accelerated linear algebra compiler (XLA), just-in-time compilation, and its seamlessly integrated automatic vectorization, auto-differentiation capabilities and GPU compatibility. Remarkably, XLuminA demonstrates a speed-up of 4 orders of magnitude compared to well-established numerical optimization methods. We showcase XLuminA's potential by rediscovering two foundational techniques in advanced microscopy, together with new superior experimental layouts. Ultimately, XLuminA identified a novel experimental blueprint featuring sub-diffraction imaging capabilities. This work constitutes and important step in AI-driven scientific discovery of new concepts in optics and advanced microscopy.