This paper introduces Gauge Flow Models, a novel class of Generative Flow Models. These models incorporate a learnable Gauge Field within the Flow Ordinary Differential Equation (ODE). A comprehensive mathematical framework for these models, detailing their construction and properties, is provided. Experiments using Flow Matching on Gaussian Mixture Models demonstrate that Gauge Flow Models yields significantly better performance than traditional Flow Models of comparable or even larger size. Additionally, unpublished research indicates a potential for enhanced performance across a broader range of generative tasks.