add SmoothStep Schedule

[Green-Sky]

While looking into the Beta Schedule implementation, I realized that beta_dist(0.6, 0.6).ppf(x) looks very close to a simple smoothstep(x) function.

This feels too simple that no one else might have thought of doing this...

see #811 ( #811 (comment) )

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Some values for 8 steps:

f(x)	beta(0.6, 0.6) ppf	smoothstep
f(1.000000)	1.000000	1.000000
f(0.875000)	0.942844	0.957031
f(0.750000)	0.824320	0.843750
f(0.625000)	0.670619	0.683594
f(0.500000)	0.500000	0.500000
f(0.375000)	0.329381	0.316406
f(0.250000)	0.175680	0.156250
f(0.125000)	0.057156	0.042969

Comparison:

beta(0.6,0.6) ppf	smoothstep

(Chroma1-HD-Flash-Q4_K_S)

[leejet]

Thank you for your contribution.

[Green-Sky]

Works great with SDXL lightning too. #198 (eg RealVisXL 5.0 Lightning).

Should work well anywhere you would choose simple or beta.

[Green-Sky]

Custom flux.1-light-8b + hyper flux 8steps merge:

euler+discrete	euler+smoothstep

It clearly eliminates most artifacts I initially put down as quantization induced. (but text quality is reduced)

details

$ result/bin/sd -m models/hyper-flux.1-lite-8B-8step-q5_k.gguf --t5xxl models/flux-extra/t5xxl_fp16.safetensors --clip_l models/flux-extra/clip_l-f16.gguf -t 8 --vae models/flux-extra/ae-f16.gguf --sampling-method euler --scheduler smoothstep --steps 8 --cfg-scale 1 -p 'Photograph of the Alps. Vivid summer afternoon. Everything is perfectly in focus.' -v -W 768 -H 768 --diffusion-fa -o hf1-lite-8b-8step-euler-smoothstep.png --clip-on-cpu --vae-conv-direct

https://huggingface.co/Green-Sky/flux.1-lite-8B-GGUF/blob/main/lora-experiments/hyper-flux.1-lite-8B-8step-q5_k.gguf

[stduhpf]

Chroma flash with Heun + Smoothstep is great.

[Green-Sky]

The comparisons for flux.1 schnell are less decisive, but I think smoothstep wins overall.

euler+discrete	euler+smoothstep

Smoothstep seems to produce higher frequency noise in the final image, which helps fine details like hair strains a lot.

Just 4 steps with q4_k is really pushing the limits of visuals in any case.