As far as I'm aware, this is the largest Normalizing Flow that exists, and I think they undermined their work by not mentioning this...
Their ImageNet model (4_1024_8_8_0.05[0]) is ~820M while AFHQ is ~472M. Prior to that there is DenseFlow[1] and MaCow[2], which are both <200M parameters. For more comparison, that makes DenseFlow and MaCow smaller than iDDPM[3] (270M params) and ADM[4] (553M for 256 unconditional). And now, it isn't uncommon for modern diffusion models to have several billion parameters![5] (from this we get some numbers on ImageNet-256, which allows a direct comparison, making TarFlow closer to MaskDiT/2 and much smaller than SimpleDiffusion and VDM++, both of which are in billions. But note that this is 128 vs 256!)
Essentially, the argument here is that you can scale (Composable) Normalizing Flows just as well as diffusion models. There's a lot of extra benefits you get too in the latent space, but that's a much longer discussion. Honestly, the TarFlow method is simple and there's probably a lot of improvements that can be made. But don't take that as a knock on this paper! I actually really appreciated it and it really set out to show what they tried to show. The real thing is just no one trained flows at this scale before and this really needs to be highlighted.
The tldr: people have really just overlooked different model architectures
[0] Used a third party reproduction so might be different but their AFHQ-256 model matches at 472M params https://github.com/encoreus/GS-Jacobi_for_TarFlow
[1] https://arxiv.org/abs/2106.04627
[2] https://arxiv.org/abs/1902.04208
[3] https://arxiv.org/abs/2102.09672
[4] https://arxiv.org/abs/2105.05233
[5] https://arxiv.org/abs/2401.11605
[Side note] Hey, if the TarFlow team is hiring, I'd love to work with you guys
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