Note: You will basically always have to tweak settings like s_noise to get a good result. If the generation looks smooth/undetailed increase s_noise somewhere. If it looks crunchy, super high contrast, etc then try reducing noise.

Nodes

ComposableSampler

Possible Parameters

avgmerge_stretch(0.4): Used for average and sample merge types. See below.
model_call_cache(unset): Caches the result of model calls. For example, Bogacki is 3 model calls per step. The first one usually depends on the merge strategy: average for example shares the first model evaluation between substeps, but subsequent model calls (i.e. Bogacki 2nd and 3rd model evaluations) still occur. When the model call cache is active, it's possible to cache those evalutions and avoid a model call for the remaining substeps. If you set model_call_cache to 1 then the result of that second call will be cached and if you're running two Bogacki substeps then the second one will use the cached version. Massively accelerates inference (especially when using the average merge strategy) but is likely very unsound and inaccurate. Does not apply to the sampler call for the sample merge strategy.
model_call_cache_threshold(1): Disables caching model call results with a call index below the threshold value (starting at 0). For example, if set to 2 and using a sampler like Bogacki that calls the model two extra times, the first will never be cached. The default value of 1 disabling caching for the first model call per substep. I generally would not recommend setting it to 0, especially with average or sample merge strategies.
model_call_cache_max_use(1000000): The number of times cache items can be re-used. The default is effectively no limit. Where would this be useful? Let's say you're using the average merge strategy and a multi step sampler that calls the model at least one more time with 50 substeps. If you set the value to 25, the model cache result will be updated around substep 25 which may produce better results than reusing the result 50 times.

Since it's kind of confusing even for me, a little more explanation: The model call cache caches results for model call indexes between model_call_cache_threshold and model_call_cache - 1. If you set model_call_cache_threshold to 0 and model_call_cache to 1 then only the first model call will be cached. If you set model_call_cache_threshold to 1 and model_call_cache to 2 then call 0 will not be cached, call 1 will be cached, call 2 will be cached, call 3 will not be cached, and so on.

Merging

When running multiple substeps per step, the results will combined based on the merge strategy. Possible strategies (in order of least weird to most weird):

divide: Creates a linear schedule between the current sigma and the next and runs the substeps in sequence. The model is called at least once per substep.
normal: The model is called at least once per substep (and possibly additional times for higher order samplers). The result of each substep is noised and the next substep uses that result. Then all the results are averaged.
average: The model is called once at the beginning of the step and substeps share that result (but it may be called additional times for higher order samplers). This means substeps for samplers like reversible Euler, Heun 1s, DPM++ 2m SDE are essentially free. May be theoretically very unsound and inaccurate, requires manual tweaking of settings like s_noise. Supports the parameter avgmerge_stretch(0.4) which basically rolls back the current sigma and adds some noise (otherwise running a substep is deterministic and there would be no point to running a sampler like Euler more than once).
sample: Like average (and uses avgmerge_stretch) but instead of simply using the average, it does a sampler step toward that instead. You can plug in any substep sampler to the merge_sampler_opt input (if unconnected and the merge method is sample then Euler will be used). Note: Substeps in the attached sampler will be ignored.
sample_uncached: Similar to sample, however it calls the model per substep instead of caching the result and sharing it. Aside from sampling toward the result, it works more like the normal merge strategy. Theoretically it should be better because it's taking less shortcuts but results seem worse.

When using average and sample merge strategies and with model call caching enabled you can get away with setting substeps super high. Running something like 100 substeps is actually quite practical and seems to work well.

ComposableStepSampler

This node has a text input for YAML (or JSON) advanced parameters.

For example, you could enter something like this in the field:

reta: 1.1
leap: 3
dyn_deta_mode: "deta"

Possible Parameters

General

eta(1.0): Will override eta in the node if set.
dyn_eta_start(unset) and dyn_eta_end(unset): No effect unless both values are set. Will interpolate between start and end based on the percentage of sampling. Note: This is a factor applied to ETA, not a flat value.
s_noise(1.0): Will override s_noise in the node if set.
solver_type(midpoint): Applies to DPM++ 2m SDE. May be one of midpoint or heun (midpoint is generally recommended).

Reversible

reta(1.0): Reverse ETA.
dyn_reta_start(unset) and dyn_reta_end(unset): No effect unless both values are set. Will interpolate between start and end based on the percentage of sampling. Note: This is a factor applied to RETA, not a flat value.

Dancing

leap(2): Distance to try to leap forward. If you set leap to 1 you just get plain old Euler ancestral.
deta(1.0): ETA used for dance steps.
dyn_deta_start(unset) and dyn_deta_end(unset): No effect unless both values are set. Will interpolate between start and end based on the percentage of sampling. Note: This is a factor applied to DETA, not a flat value.
dyn_deta_mode(lerp): May be one of:
- deta: Scales deta based on the value from dyn_deta_start/end.
- lerp: Does the dance step according to deta and then LERPs the non-dance sample result with the dance sample result based on the scale calculated from dyn_deta_start/end (which is 1.0 if they are unset). For example, if the dance scale is 0.5 you will get 50% normal sampling, 50% dancing sampling.
- lerp_alt: Similar to lerp except it LERPs with the leap result instead of a normal Euler ancestral result.

RES

res_simple_phi(false): Uses a faster but possibly less accurate method for calculating phi. What does phi do? I haven't the foggiest!
res_c2(0.5): Solver partial step size, the default of 0.5 appears to use the midpoint. Setting it to a lower value might possibly be more accurate but slower?

TTM JVP

alterate_phi_2_calc(true): Supposedly works better than disabled when ETA isn't 0. I didn't notice a difference.

Note: TTM is a weird sampler. If you're using model caching you must make sure the entries TTM uses are populated first (by having before any other samplers that call the model multiple times). It may also not work with some other model patches and upscale methods.

Credits

I can move code around but sampling math and creating samplers is far beyond my ability. I didn't write any of the original samplers:

Euler, DPMPP SDE, DPMPP 2S, DPM++ 2m, 2m SDE and 3m SDE samplers based on ComfyUI's implementation.
Reversible Heun, Reversible Heun 1s, RES, Trapezoidal, Bogacki, Reversible Bogacki, RK4 and Euler Dancing samplers based on implementation from https://github.com/Clybius/ComfyUI-Extra-Samplers
TTM JVP sampler based on implementation written by Katherine Crowson (but yoinked from the Extra-Samplers repo mentioned above).
Normal substep merge strategy based on implementation from https://github.com/Clybius/ComfyUI-Extra-Samplers

Thanks!