In order to reveal the mechanism for brazing diamond using Ag–Cu–Ti filler metal, thermoanalysis of elemental metals (silver and copper) either with added diamond micropowder or with added titanium carbide micropowder as nucleant were investigated to detect undercoolings. No undercooling for the solidification of silver with added titanium carbide powder was detected by the thermoanalytical curve, and also no undercooling for copper with added diamond powder was detected. These phenomena suggest that titanium carbide powder acts in the solidification of silver effectively as a nucleant and that diamond powder also acts in the solidification of copper as a nucleant. Fine-grained silver was observed in the micrograph of the silver added with titanium carbide powder. The results of the calculations on the planar disregistry, δ, and the dispersion energy, Edisp revealed that the Ag (100)–TiC(100) interface and Cu(100)–diamond (100) interface are more stable than the other combinations. The results of undercoolings of various specimens correlated with both planar disregistry and dispersion energy. According to these results, the titanium carbide reaction product is considered to play an important role in the solidification of silver. The brazing strength is considered to arise from the solidification of the brazing filler metal from the titanium carbide reaction product.