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Exciting advances in technologies to measure biological systems are currently at the forefront of research. The ability to gather data along an increasing number of omic dimensions has created a need for tools to analyze all of this information together, rather than siloing each technology into separate analysis pipelines. To advance this goal, we introduce a framework called the Single-Cell Multi-Modal GAN (scMMGAN) that integrates data from multiple modalities into a unified representation in the ambient data space for downstream analysis using a combination of adversarial learning and data geometry techniques. The framework’s key improvement is an additional diffusion geometry loss with a new kernel that constrains the otherwise over-parameterized GAN network. We demonstrate scMMGAN’s ability to produce more meaningful alignments than alternative methods on a wide variety of data modalities, and that its output can be used to draw conclusions from real-world biological experimental data. We highlight data from an experiment studying the development of triple negative breast cancer, where we show how scMMGAN can be used to identify novel gene associations and we demonstrate that cell clusters identified only on the scRNAseq data occur in localized spatial patterns that reveal insights on the spatial transcriptomic images.