DIPHINE is the first neural estimator that uses score-based diffusion models to jointly estimate all mutual information terms required by Integrated Information Decomposition ($Φ$ID) from a single amortized network. It recovers the sixteen non-overlapping information atoms via Möbius inversion and provides a theoretical analysis showing synergy-to-synergy estimation is the most challenging, with accurate results on synthetic benchmarks and real-world physiological data.