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Can we build continuous generative models which generalize across scales, canbe evaluated at any coordinate, admit calculation of exact derivatives, and areconceptually simple? Existing MLP-based architectures generate worse samplesthan the grid-based generators with favorable convolutional inductive biases.Models that focus on generating images at different scales do better, butemploy complex architectures not designed for continuous evaluation of imagesand derivatives. We take a signal-processing perspective and treat continuousimage generation as interpolation from samples. Indeed, correctly sampleddiscrete images contain all information about the low spatial frequencies. Thequestion is then how to extrapolate the spectrum in a data-driven way whilemeeting the above design criteria. Our answer is FunkNN -- a new convolutionalnetwork which learns how to reconstruct continuous images at arbitrarycoordinates and can be applied to any image dataset. Combined with a discretegenerative model it becomes a functional generator which can act as a prior incontinuous ill-posed inverse problems. We show that FunkNN generateshigh-quality continuous images and exhibits strong out-of-distributionperformance thanks to its patch-based design. We further showcase itsperformance in several stylized inverse problems with exact spatialderivatives.

FunkNN: Neural Interpolation for Functional Generation