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def denoise_add_noise(x, t, pred_noise, z=None):
if z is None:
z = torch.randn_like(x)
noise = betas.sqrt()[t] * z
mean = (x - pred_noise * ((1 - alphas[t]) / (1 - alphas_hat[t]).sqrt())) / alphas[t].sqrt()
return mean + noise
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