Sintering is widely used to manufacture ceramics for structural, electronic, and energy applications, but coupled densification and grain growth, material-dependent kinetics, and sparse measurements complicate predictive modeling and process design. Without reliable simulation, processing schedules are commonly developed through repeated furnace trials and post-process characterization. Here, we present Sinter-PiNDiff, a retrainable sintering physics-integrated neural differentiable framework for predicting density and grain-size evolution across ceramic systems. Two neural networks learn material-dependent densification and grain-growth coefficients within coupled sintering rate equations, while a smooth density-saturation factor attenuates densification as theoretical density is approached. The common governing structure, network architecture, and training procedure were fitted independently to published measurements for MgO, Al-doped ZnO, and CaO-doped ThO₂. Condition-wise held-out tests evaluate predictions at unseen temperatures and compositions. Sinter-PiNDiff achieved the lowest mean error in all twelve material–metric comparisons with multilayer-perceptron and residual-network baselines. For MgO, Al-doped ZnO, and CaO-doped ThO₂, respectively, density normalized root-mean-square errors were 14.6%, 10.8%, and 14.4%, and grain-size normalized root-mean-square errors were 8.6%, 12.1%, and 19.3%. Removing the evolving density from both neural-network inputs increased both density and grain-size trajectory errors in all three systems and increased ten of the twelve aggregate errors examined, supporting density-dependent kinetic feedback. Deep ensembles estimated model disagreement, although empirical coverage showed that the resulting bands were not calibrated and did not capture all model–data discrepancies. These results establish Sinter-PiNDiff as a retrainable framework for sparse-data prediction and uncertainty-informed selection of sintering conditions.