⚠️ convention clash: clean data in diffusion; noise in flow matching
\(x_t\)
the noisy sample at time \(t\)
\(x_T\)
pure noise (diffusion)
\(t\)
timestep — \(\{1..T\}\) discrete, or \([0,1]\) continuous
\(\beta_t\)
noise-schedule variance at step \(t\)
\(\alpha_t\)
\(1 - \beta_t\)
\(\bar\alpha_t\)
\(\prod_{s\le t}\alpha_s\) — cumulative signal retention
\(\epsilon\)
the Gaussian noise added
\(\epsilon_\theta\)
the noise-prediction network
\(s_\theta\)
the score network, \(\nabla_x\log p\)
\(v_\theta\)
the velocity network (v-prediction or flow matching)
\(w\)
the classifier-free guidance scale
\(\sigma(t)\)
noise level at time \(t\) (VE / EDM parameterization)
Pitfall
The \(x_0\) clash is the one that trips people up. In diffusion, \(x_0\) is the clean image and
\(x_T\) is noise; time runs forward toward noise. In flow matching, \(x_0\) is noise and \(x_1\) is
data; time runs forward toward data. This wiki follows each field's own convention on its own
page and flags the switch. Always check which direction a paper's time axis runs.
the model's discrete units, ~4 characters in English
FLOPs vs FLOP/s
Are constantly confused in the literature. "\(10^{25}\) FLOPs" is a training
budget; "\(10^{15}\) FLOP/s" is hardware throughput. This wiki always writes the rate with a slash.