Silicon physical unclonable functions (PUF) uti- lize the variation during silicon fabrication process to extract information that will be unique for each chip. There have been many recent approaches to how PUF can be used to improve security related applications. However, it is well-known that the fabrication variation has very strong spatial correlation1 and this has been pointed out as a security threat to silicon PUF. In fact, when we apply NIST’s statistical test suite for randomness [1] against the random sequences generated from a population of 125 ring oscillator (RO) PUFs [2] using classic 1-out-of-8 Coding [3], [4] and Neighbor Coding [5], none of them can pass all the tests. In this paper, we propose to decouple the unwanted systematic variation from the desired random variation through a regression-based distiller, where the basic idea is to build a model for the systematic variation so we can generate the random sequences only from the true random variation. Applying Neighbor Coding to the same benchmark data [2], our experiment shows that 2nd and 3rd order polynomials distill random sequences that pass all the NIST randomness tests. So does 4th order polynomial in the case of 1-out-of-8 Coding. Finally, we introduce two generic random sequence generation methods. The sequences they generate fail all the randomness tests, but with the help of our proposed polynomial distiller, all but one tests are passed. These results demonstrate that our method can provide statistically random PUF information and thus bolster the security characteristics of existing PUF schemes.