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In this paper we combine video compression and modern image processing methods. We construct novel iterative filter methods for prediction signals based on Partial Differential Equation (PDE)-based methods. The central idea of the signal adaptive filters is explained and demonstrated geometrically. The meaning of particular parameters is discussed in detail. Furthermore, thorough parameter tests are introduced which improve the overall bitrate savings. It is shown that these filters enhance the rate-distortion performance of the state-of-the-art hybrid video codecs. In particular, based on mathematical denoising techniques, two types of diffusion filters are constructed: a uniform diffusion filter using a fixed filter mask and a signal adaptive diffusion filter that incorporates the structures of the underlying prediction signal. The latter has the advantage of not attenuating existing edges while the uniform filter is less complex. The filters are embedded into a software based on HEVC with additional QTBT (Quadtree plus Binary Tree) and MTT (Multi-Type-Tree) block structure. Overall, the diffusion filter method achieves average bitrate savings of 2.27% for Random Access having an average encoder runtime increase of 19% and 17% decoder runtime increase. For UHD (Ultra High Definition) test sequences, bitrate savings of up to 7.36% for Random Access are accomplished.