SDEDIT: GUIDED IMAGE SYNTHESIS AND EDITING WITH STOCHASTIC DIFFERENTIAL EQUATIONS

marii

Examples of what we are doing

sdedit1png.png

More examples

sdedit2.png

The Technique

image.png

Realism vs. Faithfulness

sdeditrealvsfaith.png

Depends on noise

sdedit_prop.png

Pay special attention to \(\sigma^2(t_0)\), the while rightside increases as this value increases. The right side comes from the gaussian noise, and the noise related to our score function that we use during sampling. All of these increase as \(\sigma^2(t_0)\) increases. \(\sigma^2(t_0)\) increasesthe closer \(t_0\) is to \(T\) and is minimized at \(0\).

Proof in Appendix A.

Algorithm

sdedit_algorithm.png

• \(\epsilon\) is a distance
• \(\Delta t\) is our step, \(t_0\) is chosen
• \(t \leftarrow t_0\frac{N}{N}\) and \(t \leftarrow t_0\frac{1}{N} = \Delta t\)

Any questions?

• In equation 4 why isnt z’s in front of imaginary?

Equation 4:

\(x(t) = x(t+\Delta t)+(\sigma^2(t)-\sigma^2(t+\Delta t))s_\theta(x(t),t)\\+\sqrt{\sigma^2(t)-\sigma^2(t+\Delta t)}z\)