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spline flows

Spline flows are a class of generative normalizing flow models that use piecewise spline functions as invertible transformations to map between simple base probability distributions and complex target distributions. In standard normalizing flows, probability densities are modeled through compositions of bijective mappings; spline flows enhance the expressiveness of these mappings by employing piecewise monotonic polynomials or rational functions, such as linear, cubic, or rational-quadratic splines. Neural networks are typically used to predict the knot locations and derivative parameters that define each spline segment. This approach enables the model to capture highly nonlinear, multimodal data structures with greater flexibility than conventional affine transformations, all while maintaining analytical invertibility and tractable Jacobian determinant calculations necessary for exact density estimation and efficient sampling.

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