Molecular structure generation from mass spectrometry is fundamental for understanding cellular metabolism and discovering novel compounds. Although tandem mass spectrometry (MS/MS) enables the high-throughput acquisition of fragment fingerprints, these spectra often reflect higher-order interactions involving the concerted cleavage of multiple atoms and bonds-crucial for resolving complex isomers and non-local fragmentation mechanisms. However, most existing methods adopt atom-centric and pairwise interaction modeling, overlooking higher-order edge interactions and lacking the capacity to systematically capture essential many-body characteristics for structure generation. To overcome these limitations, we present MBGen, a Many-Body enhanced diffusion framework for de novo molecular structure Generation from mass spectra. By integrating a many-body attention mechanism and higher-order edge modeling, MBGen comprehensively leverages the rich structural information encoded in MS/MS spectra, enabling accurate de novo generation and isomer differentiation for novel molecules. Experimental results on the NPLIB1 and MassSpecGym benchmarks demonstrate that MBGen achieves superior performance, with improvements of up to 230% over state-of-the-art methods, highlighting the scientific value and practical utility of many-body modeling for mass spectrometry-based molecular generation. Further analysis and ablation studies show that our approach effectively captures higher-order interactions and exhibits enhanced sensitivity to complex isomeric and non-local fragmentation information.