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Equation 4 · Part 2 · How AI for Science and Medicine Actually Works

Symbol barα_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),
αˉt\bar{\alpha}_t

What this part means

barα_t is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

barα_t is one of the signed contributions combined to compute the quantity on the left.

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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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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