PNDM
Overview
Pseudo Numerical methods for Diffusion Models on manifolds (PNDM) by Luping Liu, Yi Ren, Zhijie Lin and Zhou Zhao.
The abstract of the paper is the following:
Denoising Diffusion Probabilistic Models (DDPMs) can generate highquality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully accelerated DDPMs through adjusting the variance schedule (e.g., Improved Denoising Diffusion Probabilistic Models) or the denoising equation (e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these acceleration methods cannot maintain the quality of samples and even introduce new noise at a high speedup rate, which limit their practicability. To accelerate the inference process while keeping the sample quality, we provide a fresh perspective that DDPMs should be treated as solving differential equations on manifolds. Under such a perspective, we propose pseudo numerical methods for diffusion models (PNDMs). Specifically, we figure out how to solve differential equations on manifolds and show that DDIMs are simple cases of pseudo numerical methods. We change several classical numerical methods to corresponding pseudo numerical methods and find that the pseudo linear multistep method is the best in most situations. According to our experiments, by directly using pretrained models on Cifar10, CelebA and LSUN, PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps (by around 0.4 in FID) and have good generalization on different variance schedules.
The original codebase can be found here.
Available Pipelines:
Pipeline  Tasks  Colab 

pipeline_pndm.py  Unconditional Image Generation   
PNDMPipeline
class diffusers.PNDMPipeline
< source >( unet: UNet2DModel scheduler: PNDMScheduler )
Parameters

unet (
UNet2DModel
) — UNet architecture to denoise the encoded image latents. 
scheduler (SchedulerMixin) —
The
PNDMScheduler
to be used in combination withunet
to denoise the encoded image.
This model inherits from DiffusionPipeline. Check the superclass documentation for the generic methods the library implements for all the pipelines (such as downloading or saving, running on a particular device, etc.)
__call__
< source >(
batch_size: int = 1
num_inference_steps: int = 50
generator: typing.Optional[torch._C.Generator] = None
output_type: typing.Optional[str] = 'pil'
return_dict: bool = True
**kwargs
)
→
ImagePipelineOutput or tuple
Parameters

batch_size (
int
,optional
, defaults to 1) — The number of images to generate. 
num_inference_steps (
int
,optional
, defaults to 50) — The number of denoising steps. More denoising steps usually lead to a higher quality image at the expense of slower inference. 
generator (
torch.Generator
,optional
) — A torch generator to make generation deterministic. 
output_type (
str
,optional
, defaults to"pil"
) — The output format of the generate image. Choose between PIL:PIL.Image.Image
ornd.array
. 
return_dict (
bool
,optional
, defaults toTrue
) — Whether or not to return a ImagePipelineOutput instead of a plain tuple.
Returns
ImagePipelineOutput or tuple
ImagePipelineOutput
if
return_dict
is True, otherwise a `tuple. When returning a tuple, the first element is a list with the
generated images.