Fix initial noise standard deviation

[kjslag]

prepare_sampling_loop in diffusionmodules/sampling.py currently initializes the initial noise with standard deviation sqrt(1+sigma^2). However, according to the EDM paper [1], the initial noise standard deviation should just be sigma. (See line 2 of Algorithm 2 of "Elucidating the Design Space of Diffusion-Based Generative Models".) This pull request fixes the issue.

I tested the change using the code below:

import importlib
import numpy
import torch
import torchvision

import sgm
import sgm.inference.api as api

pipeline = api.SamplingPipeline(api.ModelArchitecture.SDXL_V1_BASE)

torch.manual_seed(1)
output = pipeline.text_to_image(
    params=api.SamplingParams(steps=10),
    prompt="A professional photograph of an astronaut riding a pig")
torchvision.utils.save_image(output[0], 'image.png')

Below are the results. Note that after the fix, there are several improvements:

• an extra leg is removed behind the pig's front left leg
• pig's right eye no longer unrealistically pops out of the pig's face
• better pig nose
• better pig tail
• back of astronaut helmet doesn't look as strange
• the patch on the right of the astronaut's shoulder is no longer blurry

This is the only test I bothered trying. More tests/checks may be warranted...

Before the fix:

After the fix: