Update sd_schedulers.py

[unicornsyay]

Implement Karras Exponential Scheduler for Enhanced Sigma Blending in Diffusion Models

This commit introduces the Karras Exponential Scheduler function, which blends sigma values generated by the Karras and Exponential scheduling methods. The primary objective is to enhance the noise schedule during the diffusion process, improving image generation quality, convergence speed, and maintaining structural details, particularly for img2img tasks.

What is the Karras Exponential Scheduler?
The Karras Exponential Scheduler is a method that dynamically blends two distinct scheduling approaches—Karras and Exponential—to create a combined noise schedule for diffusion models.

Karras Scheduling: A method known for its ability to generate high-quality images by spacing noise levels in a way that emphasizes low-noise areas, leading to more detailed and coherent images.

Exponential Scheduling: Emphasizes a more gradual reduction of noise, providing a smoother transition that can help in areas where the model requires more flexibility to explore variations. By blending these two methods, the scheduler creates a noise schedule that leverages the strengths of both approaches, leading to better overall performance during image generation.

Why Use the Karras Exponential Scheduler?
Improved Convergence: The blended approach allows the model to converge more quickly on high-quality results, reducing artifacts commonly seen in traditional img2img and initial image generation tasks.

Enhanced Structural Preservation: By combining Karras's focus on detail preservation with Exponential’s smoother transitions, this scheduler helps maintain critical features, such as faces, hands, and complex object structures, which are often lost in purely exponential or linear scheduling.

Dynamic Blending for Flexibility: The scheduler employs a dynamic blend factor that adjusts the influence of each method throughout the diffusion process, providing a more adaptive approach to image generation.

Sharpening Mechanism: An additional sharpening factor is applied to adjust the impact of low noise levels, fine-tuning the result and preventing over-smoothing of fine details.

Key Changes Introduced:
karras_exponential_scheduler Function: Blends Karras and Exponential sigma sequences based on a dynamic blend factor that adjusts during the diffusion process. Sharpening Feature: Applies conditional sharpening to low-value sigmas to maintain image sharpness and prevent loss of detail. Error Handling: Robust error handling with fallback options ensures stable performance even when unexpected input issues occur.

Benefits:
Better Quality: Results in cleaner, more coherent images with less distortion, particularly noticeable in img2img scenarios. Increased Control: Provides additional tuning options via blend_factor and sharpen_factor, allowing for fine-grained adjustments based on the specific task.

Stability: Error handling ensures the model continues to function even when generation challenges arise, offering fallback sigmas to maintain consistency.

Usage:
This scheduler can be directly integrated into diffusion pipelines and used as an alternative to existing sigma scheduling methods, particularly where traditional schedules struggle with img2img or high-detail preservation.

This addition aims to improve the overall robustness and versatility of diffusion models, making them more effective in real-world applications requiring high detail retention and image consistency.

Description

• a simple description of what you're trying to accomplish
• a summary of changes in code
• which issues it fixes, if any

Screenshots/videos:

Checklist:

• I have read contributing wiki page
• I have performed a self-review of my own code
• My code follows the style guidelines
• My code passes tests

[unicornsyay]

It converges faster than regular karras or exponential, but it requires noise injection during img2img. If you don't uuse noise injection (I use 0.3 with 0.4 denoising), then it tends to overfit and details like fingers, toes, or even arms can go missing. It performs best at img2img when you inject noise. You can tweak the values for blending, sharpen_factor or sigma max. The values I left seem to work the best.

[unicornsyay]

I see that it was referencing a function which no longer exists. I will have to review, make changes, then commit again.