Unofficial ComfyUI nodes for restart sampling based on the paper "Restart Sampling for Improving Generative Processes"

Paper: https://arxiv.org/abs/2306.14878

Repo: https://github.com/Newbeeer/diffusion_restart_sampling

This has been tested for ComfyUI for the following commit: d14bdb1

Enter the following command from the commandline starting in ComfyUI/custom_nodes/

git clone https://github.com/ssitu/ComfyUI_restart_sampling

The Restart sampler nodes can be found in the node menu under sampling.

If you set the environment variable COMFYUI_VERBOSE_RESTART_SAMPLING to 1, restart sampling will dump information about the steps it's going to run to the console.

Node	Image	Description
KSampler With Restarts		Has all the inputs of a KSampler, but with an added string widget for configuring the Restart segments and a widget for the scheduler for the Restart segments. Not all samplers and schedulers from KSampler are currently supported. Restart sampling is done with ODE samplers and are not supposed to be used with SDE samplers. See the Segments section below for information how to define segments. For more information on the Restart parameters, refer to the paper. The restart_scheduler is used as the scheduler for the denoising process during restart segments. The researchers used the Karras scheduler in their experiments, but use the same scheduler as the sampler schedule in their implementation.
KSampler With Restarts (Simple)		Instead of having a restart segment scheduler, segments will use the same scheduler as the KSampler scheduler.
KSampler With Restarts (Advanced)		Has all the inputs for an Advanced KSampler with all the inputs for restart sampling. It should be noted that there is a possibility for invalid segments when using it to end the denoising process early or starting it late (e.g. 20 steps, start at step 0, end at step 10) and invalid segments will be ignored. An invalid segment means that the closest $t_{\textrm{min}}$ in the noise schedule is higher than the segment's $t_{\textrm{max}}$, so the segment would have restarted the denoising process at $t_{\textrm{max}}$ then try to go to a higher noise level (when it should've gone to a lower noise level near $t_{\textrm{min}}$) which will destroy the sample.
KSampler With Restarts (Custom)		Essentially the same as KSampler With Restarts (Advanced) but it takes a SAMPLER input like the built in SamplerCustom node. Note that it is possible to input samplers that don't work properly or are incompatible with Restart sampling like SDE and UniPC samplers.

The format for segments is a sequence of comma separated arrays of ${[N_{\textrm{Restart}}, K, t_{\textrm{min}}, t_{\textrm{max}}]}$. For example, [4, 1, 19.35, 40.79], [4, 1, 1.09, 1.92], [4, 5, 0.59, 1.09], [4, 5, 0.30, 0.59], [6, 6, 0.06, 0.30] would be a valid sequence. Segments may overwrite each other if their $t_{\textrm{min}}$ parameters are too close to each other. Each segment will add $(N_{\textrm{Restart}} - 1) \cdot K$ steps to the sampling process.

Both $t_{\textrm{min}}$ and $t_{\textrm{max}}$ within a segment definition may be specified in any of the following three ways:

• A positive numeric value (i.e. 1.2) — this will be interpreted as a sigma value.
• A negative numeric value between -0 and -1000 — this will be interpeted as a (positive) timestep. Timesteps will be converted to integer values so if you need to specify timestep 0 you can do something like -0.1.
• A quoted string percentage value followed by a percent sign (i.e. "25%") — note that this refers to the percentage of sampling, not the percentage of steps that have elapsed.

You may freely mix the different formats. For example, [2, 2, -500, "10%"], [3, 2, 5.3, -3] would be a valid sequence. Note: Random numbers used for example only, not recommended.

Special segment values:

• Enter default to use the default segment list.
• Enter a1111 to emulate A1111 WebUI's segment calculation behavior. For full emulation, enabled chunked mode, set both schedulers to karras and the sampler to heun.

When chunked mode is enabled, the sampler is called with as many steps as possible up to the next segment. When disabled, the sampler is only called with a single step at a time. Some samplers such as SDE samplers, momentum samplers, second order samplers like dpmpp_2m use state from previous steps - when called step-by-step, this state is lost. Using chunked mode may make those samplers more accurate.

Note: Using SDE or momentum samplers with restart is likely not an improvement over normal sampling.

Consider the default segments of [3,2,0.06,0.30],[3,1,0.30,0.59].

1. $N_{\textrm{Restart}}=3, {K}=2, t_{\textrm{min}}=0.06, t_{\textrm{max}}=0.30$ — closer to the end of sampling, will run two restarts two times.
2. $N_{\textrm{Restart}}=3, {K}=1, t_{\textrm{min}}=0.30, t_{\textrm{max}}=0.59$ — closer to the beginning of sampling, will run two restarts one time.

Running 20 steps with normal scheduling will look something like this:

Step   1: sigma=10.7
Step   2: sigma=8.08
Step   3: sigma=6.2
[... elided for brevity]
Step  15: sigma=0.596
Step  16: sigma=0.474
Step  17: sigma=0.356 -- [3,1,0.30,0.59] matches here.
  K=1:
    restart 1, step 18
    restart 2, step 19
Step  20: sigma=0.232
Step  21: sigma=0.0292 -- [3,2,0.06,0.30] matches here.
  K=1:
    restart 1, step 22
    restart 2, step 23
  K=2:
    restart 1, step 24
    restart 2, step 25
Step  26: sigma=0.0