sigmas_tools_and_the_golden_scheduler

A few nodes to mix sigmas and a custom scheduler that uses phi, then one using eval() to be able to schedule with custom formulas.

Nodes

Merge sigmas by average: takes sigmas_1 and sigmas_2 as an input and merge them with a custom weight.

Merge sigmas gradually : takes sigmas_1 and sigmas_2 as an input and merge them by starting with sigmas_1 times the weight and sigmas_2 times 1-the weight, like if you want to start with karras and end with simple.

Multiply sigmas: simply multiply the sigmas by what you want.

Split and concatenate sigmas: takes sigmas_1 and sigmas_2 as an input and merge them by starting with sigmas_1 until the chosen step, then the rest with sigmas_2

Get sigmas as float: Just get first - last step to be able to inject noise inside a latent with noise injection nodes.

Graph sigmas: make a graph of the sigmas.

Aligned scheduler: selects the steps from align your steps.

Differences:

• force_sigma_min: off / 10 steps: gives the same values as Comfy's implementation, which matches the aligned steps of the simple scheduler.
• force_sigma_min: on / 11 steps: the added step corresponds to the minimum sigmas of the model.
• The main difference is that it takes into account the min/max sigmas of the model rather than those from the linked page. This might be beneficial with COSXL models for example.

Manual scheduler: uses eval() to create a custom schedule. The math module is fully imported. Available variables are:

• sigmin: sigma min
• sigmax: sigma max
• phi
• pi comes from math
• x equals 1 for the first step and 0 for the last step.
• y equals 0 for the first step and 1 for the last step.
• s or steps: total amount of steps.
• j from 0 to total steps -1.
• f gives a normalized from 1 to 0 curve based on a reversed Fibonacci sequence

And this one makes the max sigma proportional to the amount of steps, it is pretty good with dpmpp2m:

max([x**phi*s/phi,sigmin])

This one works nicely with lms, euler and dpmpp2m NOW ALSO WITH dpmpp2m_sde if you toggle the sgm button:

x**((x+1)*phi)*sigmax+y**((x+1)*phi)*sigmin

Here is how the graphs look like:

The Golden Scheduler: Uses phi as the exponent. Hence the name 😊. The formula is pretty simple:

(1-x/(steps-1))**phi*sigmax+(x/(steps-1))**phi*sigmin for x in range(steps)

Where x it the iteration variable for the steps.

Or if you want to use it in the manual node:

x**phi*sigmax+y**phi*sigmin

It works pretty well with dpmpp2m, euler and lms!

The karras formula can be written like this:

(sigmax ** (1 / 7) + y * (sigmin ** (1 / 7) - sigmax ** (1 / 7))) ** 7

Using tau:

(sigmax ** (1 / tau) + y * (sigmin ** (1 / tau) - sigmax ** (1 / tau))) ** tau

With a formula based on the fibonacci sequence:

(sigmax-sigmin)*f**(1/2)+sigmin

More steps means a steeper curve.

Example with this formula:

Here is a comparison, the golden scheduler, using my model Iris Lux :

Karras:

Here is a mix using dpmpp3m_sde with 50% exponential, 25% simple and 25% sgm uniform: