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Undifferentiated sarcomas (USARCs) of adults are diverse, rare, and aggressive soft tissue cancers. Recent sequencing efforts have confirmed that USARCs exhibit one of the highest burdens of structural aberrations across human cancer. Here, we sought to unravel the molecular basis of the structural complexity in USARCs by integrating DNA sequencing, ploidy analysis, gene expression, and methylation profiling. We identified whole genome duplication as a prevalent and pernicious force in USARC tumorigenesis. Using mathematical deconvolution strategies to unravel the complex copy-number profiles and mutational timing models we infer distinct evolutionary pathways of these rare cancers. In addition, 15% of tumors exhibited raised mutational burdens that correlated with gene expression signatures of immune infiltration, and good prognosis.