$$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \hat{x}_0 = f_\theta(x_t, t)$$

Equation 4 · AI for Science

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The larger change is in how coordinates are produced. Rather than a Structure Module built on rotations and translations, AlphaFold3 uses a diffusion module that operates directly on raw atom coordinates and a coarse token representation, without rotational frames at all. Diffusion models are trained on a simple, general task: take a true data point, corrupt it with noise at a known level, and train a network to recover the original from the corrupted version. For coordinates $x_0$ noised to $x_t$ at noise level t , $x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \hat{x}_0 = f_\theta(x_t, t)$. with $\epsilon$ drawn from a standard normal distribution and $f_\theta$ the trained network. Generating a structure then means starting from coordinates that are…

Meanings in this article

• $x_t$: a coordinate in the stated process.
• $x_0$: a coordinate in the stated process.
• $\epsilon$: a random quantity drawn from a standard normal distribution.
• $f_\theta$: the trained network.
• $t$: the noise-level index.

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