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Equation 4 · Part 8 · How AI for Science and Medicine Actually Works

=

xt=αˉt x0+1−αˉt ϵ,x^0=fθ(xt,t),x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \hat{x}_0 = f_\theta(x_t, t),
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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 x0x_0 noised to xtx_t at noise level t , xt=αˉt x0+1−αˉt ϵ,x^0=fθ(xt,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 ϵ\epsilon drawn from a standard normal distribution and fθf_\theta the trained network. Generating a structure then means starting from coordinates that are…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.