← All parts of this equation

Equation 12 · Part 7 · Adapters, Native Pretraining, and Unified Tokens: The Main Multimodal Architectures, Compared

Symbol c

Ldiffusion=Ex0, ϵ∼N(0,I), t[ ∥ϵ−ϵθ(xt,t,c)∥2 ],xt=αˉt x0+1−αˉt ϵ\mathcal{L}_{\text{diffusion}} = \mathbb{E}_{x_0,\, \epsilon \sim \mathcal{N}(0, I),\, t} \Big[\, \big\| \epsilon - \epsilon_\theta(x_t, t, c) \big\|^2 \,\Big], \qquad x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1 - \bar{\alpha}_t}\, \epsilon
cc

What this part means

a conditioning signal — most often a text embedding — and generation runs the process in reverse, starting from pure noise and repeatedly subtracting a predicted noise estimate.

Its job in the formula

c appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

Where the article explains it

where c is a conditioning signal — most often a text embedding — and generation runs the process in reverse, starting from pure noise and repeatedly subtracting a predicted noise estimate.

The passage around this formula

…use next-token prediction at all. A diffusion model learns to reverse a fixed process that gradually adds Gaussian noise to data, training a network to predict the noise component at each step: Ldiffusion=Ex0, ϵ∼N(0,I), t[ ∥ϵ−ϵθ(xt,t,c)∥2 ],xt=αˉt x0+1−αˉt ϵ\mathcal{L}_{\text{diffusion}} = \mathbb{E}_{x_0,\, \epsilon \sim \mathcal{N}(0, I),\, t} \Big[\, \big\| \epsilon - \epsilon_\theta(x_t, t, c) \big\|^2 \,\Big], \qquad x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1 - \bar{\alpha}_t}\, \epsilon. where c is a conditioning signal — most often a text embedding — and generation runs the process in reverse, starting from pure noise and repeatedly subtracting a predicted noise estimate.

Read this part in the article →

Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the article section

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