A confusion comparing code with paper

[SuX97]

Hi, authors:

Great work! While, I'm a bit confused about the description and code, in paper A.5:

x_t is called noisy image. However, in code,

        if self.cfg.recon_loss:
            # reconstruct x0
            latents_recon = self.model.predict_start_from_noise(
                latents_noisy, t, noise_pred
            )
            # x0-reconstruction loss from Sec 3.2 and Appendix
            loss = (
                0.5
                * F.mse_loss(latents, latents_recon.detach(), reduction="sum")
                / latents.shape[0]
            )
            grad = torch.autograd.grad(loss, latents, retain_graph=True)[0]

x_0, x_t is actually latent after vae and noisy latent, if correct.

There do exist methods that apply loss on image-space such as HiFA, and ReconFusion, which may be confusing.

Please clearify that I'm understanding it right, Thanks!