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Well, this isn't probably a problem with the model, but the source frame having wrong eye gaze. Besides, perceptually lossless need not be defined in a side-by-side comparison context. If you were only viewing the right hand side video, how could you tell the eye gaze is off? The point was more on that the movement looks natural, unlike almost all neural avatars up to this year.
This is my field as well, although I come from the neural network angle.
Learned video codecs definitely do look promising: Microsoft's DCVC-FM (https://github.com/microsoft/DCVC) beats H.267 in BD-rate. Another benefit of the learned approach is being able to run on soon commodity NPUs, without special hardware accommodation requirements.
In the CLIC challenge, hybrid codecs (traditional + learned components) are so far the best, so that has been a letdown for pure end to end learned codecs, agree. But something like H.267 is currently not cheap to run either.
If you look at the winners of the Hutter prize, or especially the Large Text Compression Benchmark, then almost every approach uses some kind of machine learning approach for the adaptive probability model and then either arithmetic coding or rANS to losslessly encode it.
This is intuitive, as the competition organisers say: compression is prediction.
Exactly, in practice the alternatives are either blocky artifacts (JPEG and most other traditional codecs), blurring everything (learned codecs optimised for MSE) or "hallucinating" patterns when using models like GANs. However, in practice even the generative side of compression models is evaluated against the original image rather than only output quality, so the outputs tend to be passable.
To see what a lossy generator hallucinating patterns means in practice, I recommend viewing HiFiC vs original here: https://hific.github.io/