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Parametric Bidirectional Scattering Distribution Functions (BSDFs) are pervasively used because of their flexibility to represent a large variety of material appearances by simply tuning the parameters. While efficient evaluation of parametric BSDFs has been well-studied, high-quality importance sampling techniques for parametric BSDFs are still scarce. Existing sampling strategies either heavily rely on approximations, resulting in high variance, or solely perform sampling on a portion of the whole BSDF slice. Moreover, many of the sampling approaches are specifically paired with certain types of BSDFs. In this paper, we seek an efficient and general way for importance sampling parametric BSDFs. We notice that the nature of importance sampling is the mapping between a uniform distribution and the target distribution. Specifically, when BSDF parameters are given, the mapping that performs importance sampling on a BSDF slice can be simply recorded as a 2D image that we name as importance map. Following this observation, we accurately precompute the importance maps using a mathematical tool named optimal transport. Then we propose a lightweight neural network to efficiently compress the precomputed importance maps. In this way, we have brought parametric BSDF important sampling to the precomputation stage, avoiding heavy runtime computation. Since this process is similar to light baking where a set of images are precomputed, we name our method importance baking. Together with a BSDF evaluation network and a PDF (probability density function) query network, our method enables full multiple importance sampling (MIS) without any revision to the rendering pipeline. Our method essentially performs perfect importance sampling. Compared with previous methods, we demonstrate reduced noise levels on rendering results with a rich set of appearances.