Describe the bug

If you run 3n-1 steps(11, 14, ...) generation using DPMSolverSinglestepScheduler with solver_order=3, it will produce NaN output on final step.
I tried to debug what went wrong and found that in this case executes second order update on zero sigma:
[singlestep_dpm_solver_second_order_update] self.step_index=10 len(self.sigmas)=12 sigma_t=tensor(0.) sigma_s0=tensor(0.3235) sigma_s1=tensor(0.5293)
Then this zero value passed to:
lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
Where we got -inf and it broke all calculations.

Looks like last_sigmas_type='zero' not handled properly, I fixed it locally by copying handling of this case from multistep scheduler:

        # Improve numerical stability for small number of steps
        lower_order_final = (self.step_index == len(self.timesteps) - 1) and (
            (self.config.lower_order_final and len(self.timesteps) < 15)
            or self.config.final_sigmas_type == "zero"
        )
        lower_order_second = (
            (self.step_index == len(self.timesteps) - 2) and self.config.lower_order_final and len(self.timesteps) < 15
        )

        if lower_order_final:
            order = 1
        elif lower_order_second:
            order = 2 # probably should min(2, self.config.solver_order)

        prev_sample = self.singlestep_dpm_solver_update(self.model_outputs, sample=self.sample, order=order)

Upd:
Also as I can see - there no support for sde in third order update both in DPMSolverSinglestepScheduler and DPMSolverMultistepScheduler schedulers, so that with algorithm_type='sde-dpmsolver++' set they both throw error:
UnboundLocalError: local variable 'x_t' referenced before assignment
Because there no branch to handle sde algo.

Reproduction

from diffusers import StableDiffusionPipeline, DPMSolverSinglestepScheduler 
import torch

model_id = "runwayml/stable-diffusion-v1-5"
pipe = StableDiffusionPipeline.from_pretrained(model_id, torch_dtype=torch.float16)

pipe.scheduler = DPMSolverSinglestepScheduler.from_config({**pipe.scheduler.config, "solver_order":3})
pipe = pipe.to("cuda")

prompt = "a photo of an astronaut riding a horse on mars"
image = pipe(prompt, num_inference_steps=11).images[0]  
    
image.save("astronaut_rides_horse.png")

Logs

No response

System Info

• diffusers version: 0.27.2
• Platform: Windows-10-10.0.19045-SP0
• Python version: 3.10.6
• PyTorch version (GPU?): 2.2.2+cu118 (True)
• Huggingface_hub version: 0.23.1
• Transformers version: 4.41.1
• Accelerate version: 0.30.1
• xFormers version: not installed
• Using GPU in script?: Yes, RTX 3080
• Using distributed or parallel set-up in script?: ???

Who can help?

@yiyixuxu