DISCO-DJ performs large-scale structure (LSS) cosmological simulations with full support for automatic differentiation via the JAX (ascl:2111.002) ecosystem. It integrates a suite of modern cosmological modelling tools, including a fast particle-mesh (PM) N-body solver enhanced by theory-informed time integrators, such as BullFrog and FastPM (ascl:1905.010), and discreteness-suppression techniques (e.g., de-aliasing, sheet-based resampling, higher-order mass assignment kernels). The code also provides an interface to a differentiable Einstein–Boltzmann solver, high-order Lagrangian perturbation theory (nLPT) recursion relations, and semi-classical propagator perturbation theory (PPT). By utilizing JAX’s forward- and reverse-mode automatic differentiation (including memory-efficient adjoint methods), DISCO-DJ enables cosmological inference scenarios where differentiable pipelines from initial conditions to late-time observables are required.