Implementation of DALL-E 2, OpenAI's updated text-to-image synthesis neural network, in Pytorch.
Yannic Kilcher summary | AssemblyAI explainer
The main novelty seems to be an extra layer of indirection with the prior network (whether it is an autoregressive transformer or a diffusion network), which predicts an image embedding based on the text embedding from CLIP. Specifically, this repository will only build out the diffusion prior network, as it is the best performing variant (but which incidentally involves a causal transformer as the denoising network 😂)
This model is SOTA for text-to-image for now.
Please join if you are interested in helping out with the replication
There was enough interest for a Jax version. I will also eventually extend this to text to video, once the repository is in a good place.
$ pip install dalle2-pytorch
To train DALLE-2 is a 3 step process, with the training of CLIP being the most important
To train CLIP, you can either use x-clip package, or join the LAION discord, where a lot of replication efforts are already underway.
This repository will demonstrate integration with x-clip
for starters
import torch
from dalle2_pytorch import CLIP
clip = CLIP(
dim_text = 512,
dim_image = 512,
dim_latent = 512,
num_text_tokens = 49408,
text_enc_depth = 1,
text_seq_len = 256,
text_heads = 8,
visual_enc_depth = 1,
visual_image_size = 256,
visual_patch_size = 32,
visual_heads = 8,
use_all_token_embeds = True, # whether to use fine-grained contrastive learning (FILIP)
decoupled_contrastive_learning = True, # use decoupled contrastive learning (DCL) objective function, removing positive pairs from the denominator of the InfoNCE loss (CLOOB + DCL)
extra_latent_projection = True, # whether to use separate projections for text-to-image vs image-to-text comparisons (CLOOB)
use_visual_ssl = True, # whether to do self supervised learning on images
visual_ssl_type = 'simclr', # can be either 'simclr' or 'simsiam', depending on using DeCLIP or SLIP
use_mlm = False, # use masked language learning (MLM) on text (DeCLIP)
text_ssl_loss_weight = 0.05, # weight for text MLM loss
image_ssl_loss_weight = 0.05 # weight for image self-supervised learning loss
).cuda()
# mock data
text = torch.randint(0, 49408, (4, 256)).cuda()
images = torch.randn(4, 3, 256, 256).cuda()
# train
loss = clip(
text,
images,
return_loss = True # needs to be set to True to return contrastive loss
)
loss.backward()
# do the above with as many texts and images as possible in a loop
Then, you will need to train the decoder, which learns to generate images based on the image embedding coming from the trained CLIP above
import torch
from dalle2_pytorch import Unet, Decoder, CLIP
# trained clip from step 1
clip = CLIP(
dim_text = 512,
dim_image = 512,
dim_latent = 512,
num_text_tokens = 49408,
text_enc_depth = 1,
text_seq_len = 256,
text_heads = 8,
visual_enc_depth = 1,
visual_image_size = 256,
visual_patch_size = 32,
visual_heads = 8
).cuda()
# unet for the decoder
unet = Unet(
dim = 128,
image_embed_dim = 512,
cond_dim = 128,
channels = 3,
dim_mults=(1, 2, 4, 8)
).cuda()
# decoder, which contains the unet and clip
decoder = Decoder(
unet = unet,
clip = clip,
timesteps = 100,
image_cond_drop_prob = 0.1,
text_cond_drop_prob = 0.5
).cuda()
# mock images (get a lot of this)
images = torch.randn(4, 3, 256, 256).cuda()
# feed images into decoder
loss = decoder(images)
loss.backward()
# do the above for many many many many steps
# then it will learn to generate images based on the CLIP image embeddings
Finally, the main contribution of the paper. The repository offers the diffusion prior network. It takes the CLIP text embeddings and tries to generate the CLIP image embeddings. Again, you will need the trained CLIP from the first step
import torch
from dalle2_pytorch import DiffusionPriorNetwork, DiffusionPrior, CLIP
# get trained CLIP from step one
clip = CLIP(
dim_text = 512,
dim_image = 512,
dim_latent = 512,
num_text_tokens = 49408,
text_enc_depth = 6,
text_seq_len = 256,
text_heads = 8,
visual_enc_depth = 6,
visual_image_size = 256,
visual_patch_size = 32,
visual_heads = 8,
).cuda()
# setup prior network, which contains an autoregressive transformer
prior_network = DiffusionPriorNetwork(
dim = 512,
depth = 6,
dim_head = 64,
heads = 8
).cuda()
# diffusion prior network, which contains the CLIP and network (with transformer) above
diffusion_prior = DiffusionPrior(
net = prior_network,
clip = clip,
timesteps = 100,
cond_drop_prob = 0.2
).cuda()
# mock data
text = torch.randint(0, 49408, (4, 256)).cuda()
images = torch.randn(4, 3, 256, 256).cuda()
# feed text and images into diffusion prior network
loss = diffusion_prior(text, images)
loss.backward()
# do the above for many many many steps
# now the diffusion prior can generate image embeddings from the text embeddings
In the paper, they actually used a recently discovered technique, from Jonathan Ho himself (original author of DDPMs, the core technique used in DALL-E v2) for high resolution image synthesis.
This can easily be used within this framework as so
import torch
from dalle2_pytorch import Unet, Decoder, CLIP
# trained clip from step 1
clip = CLIP(
dim_text = 512,
dim_image = 512,
dim_latent = 512,
num_text_tokens = 49408,
text_enc_depth = 6,
text_seq_len = 256,
text_heads = 8,
visual_enc_depth = 6,
visual_image_size = 256,
visual_patch_size = 32,
visual_heads = 8
).cuda()
# 2 unets for the decoder (a la cascading DDPM)
unet1 = Unet(
dim = 32,
image_embed_dim = 512,
cond_dim = 128,
channels = 3,
dim_mults = (1, 2, 4, 8)
).cuda()
unet2 = Unet(
dim = 32,
image_embed_dim = 512,
cond_dim = 128,
channels = 3,
dim_mults = (1, 2, 4, 8, 16)
).cuda()
# decoder, which contains the unet(s) and clip
decoder = Decoder(
clip = clip,
unet = (unet1, unet2), # insert both unets in order of low resolution to highest resolution (you can have as many stages as you want here)
image_sizes = (256, 512), # resolutions, 256 for first unet, 512 for second. these must be unique and in ascending order (matches with the unets passed in)
timesteps = 1000,
image_cond_drop_prob = 0.1,
text_cond_drop_prob = 0.5
).cuda()
# mock images (get a lot of this)
images = torch.randn(4, 3, 512, 512).cuda()
# feed images into decoder, specifying which unet you want to train
# each unet can be trained separately, which is one of the benefits of the cascading DDPM scheme
loss = decoder(images, unet_number = 1)
loss.backward()
loss = decoder(images, unet_number = 2)
loss.backward()
# do the above for many steps for both unets
Finally, to generate the DALL-E2 images from text. Insert the trained DiffusionPrior
as well as the Decoder
(which wraps CLIP
, the causal transformer, and unet(s))
from dalle2_pytorch import DALLE2
dalle2 = DALLE2(
prior = diffusion_prior,
decoder = decoder
)
# send the text as a string if you want to use the simple tokenizer from DALLE v1
# or you can do it as token ids, if you have your own tokenizer
texts = ['glistening morning dew on a flower petal']
images = dalle2(texts) # (1, 3, 256, 256)
That's it!
Let's see the whole script below
import torch
from dalle2_pytorch import DALLE2, DiffusionPriorNetwork, DiffusionPrior, Unet, Decoder, CLIP
clip = CLIP(
dim_text = 512,
dim_image = 512,
dim_latent = 512,
num_text_tokens = 49408,
text_enc_depth = 6,
text_seq_len = 256,
text_heads = 8,
visual_enc_depth = 6,
visual_image_size = 256,
visual_patch_size = 32,
visual_heads = 8
).cuda()
# mock data
text = torch.randint(0, 49408, (4, 256)).cuda()
images = torch.randn(4, 3, 256, 256).cuda()
# train
loss = clip(
text,
images,
return_loss = True
)
loss.backward()
# do above for many steps ...
# prior networks (with transformer)
prior_network = DiffusionPriorNetwork(
dim = 512,
depth = 6,
dim_head = 64,
heads = 8
).cuda()
diffusion_prior = DiffusionPrior(
net = prior_network,
clip = clip,
timesteps = 100,
cond_drop_prob = 0.2
).cuda()
loss = diffusion_prior(text, images)
loss.backward()
# do above for many steps ...
# decoder (with unet)
unet1 = Unet(
dim = 128,
image_embed_dim = 512,
cond_dim = 128,
channels = 3,
dim_mults=(1, 2, 4, 8)
).cuda()
unet2 = Unet(
dim = 16,
image_embed_dim = 512,
cond_dim = 128,
channels = 3,
dim_mults = (1, 2, 4, 8, 16)
).cuda()
decoder = Decoder(
unet = (unet1, unet2),
image_sizes = (128, 256),
clip = clip,
timesteps = 100,
image_cond_drop_prob = 0.1,
text_cond_drop_prob = 0.5,
condition_on_text_encodings = False # set this to True if you wish to condition on text during training and sampling
).cuda()
for unet_number in (1, 2):
loss = decoder(images, unet_number = unet_number) # this can optionally be decoder(images, text) if you wish to condition on the text encodings as well, though it was hinted in the paper it didn't do much
loss.backward()
# do above for many steps
dalle2 = DALLE2(
prior = diffusion_prior,
decoder = decoder
)
images = dalle2(
['cute puppy chasing after a squirrel'],
cond_scale = 2. # classifier free guidance strength (> 1 would strengthen the condition)
)
# save your image (in this example, of size 256x256)
Everything in this readme should run without error
You can also train the decoder on images of greater than the size (say 512x512) at which CLIP was trained (256x256). The images will be resized to CLIP image resolution for the image embeddings
For the layperson, no worries, training will all be automated into a CLI tool, at least for small scale training.
It is likely, when scaling up, that you would first preprocess your images and text into corresponding embeddings before training the prior network. You can do so easily by simply passing in image_embed
, text_embed
, and optionally text_encodings
and text_mask
Working example below
import torch
from dalle2_pytorch import DiffusionPriorNetwork, DiffusionPrior, CLIP
# get trained CLIP from step one
clip = CLIP(
dim_text = 512,
dim_image = 512,
dim_latent = 512,
num_text_tokens = 49408,
text_enc_depth = 6,
text_seq_len = 256,
text_heads = 8,
visual_enc_depth = 6,
visual_image_size = 256,
visual_patch_size = 32,
visual_heads = 8,
).cuda()
# setup prior network, which contains an autoregressive transformer
prior_network = DiffusionPriorNetwork(
dim = 512,
depth = 6,
dim_head = 64,
heads = 8
).cuda()
# diffusion prior network, which contains the CLIP and network (with transformer) above
diffusion_prior = DiffusionPrior(
net = prior_network,
clip = clip,
timesteps = 100,
cond_drop_prob = 0.2,
condition_on_text_encodings = False # this probably should be true, but just to get Laion started
).cuda()
# mock data
text = torch.randint(0, 49408, (4, 256)).cuda()
images = torch.randn(4, 3, 256, 256).cuda()
# precompute the text and image embeddings
# here using the diffusion prior class, but could be done with CLIP alone
clip_image_embeds = diffusion_prior.clip.embed_image(images).image_embed
clip_text_embeds = diffusion_prior.clip.embed_text(text).text_embed
# feed text and images into diffusion prior network
loss = diffusion_prior(
text_embed = clip_text_embeds,
image_embed = clip_image_embeds
)
loss.backward()
# do the above for many many many steps
# now the diffusion prior can generate image embeddings from the text embeddings
You can also completely go CLIP
-less, in which case you will need to pass in the image_embed_dim
into the DiffusionPrior
on initialization
import torch
from dalle2_pytorch import DiffusionPriorNetwork, DiffusionPrior
# setup prior network, which contains an autoregressive transformer
prior_network = DiffusionPriorNetwork(
dim = 512,
depth = 6,
dim_head = 64,
heads = 8
).cuda()
# diffusion prior network, which contains the CLIP and network (with transformer) above
diffusion_prior = DiffusionPrior(
net = prior_network,
image_embed_dim = 512, # this needs to be set
timesteps = 100,
cond_drop_prob = 0.2,
condition_on_text_encodings = False # this probably should be true, but just to get Laion started
).cuda()
# mock data
text = torch.randint(0, 49408, (4, 256)).cuda()
images = torch.randn(4, 3, 256, 256).cuda()
# precompute the text and image embeddings
# here using the diffusion prior class, but could be done with CLIP alone
clip_image_embeds = torch.randn(4, 512).cuda()
clip_text_embeds = torch.randn(4, 512).cuda()
# feed text and images into diffusion prior network
loss = diffusion_prior(
text_embed = clip_text_embeds,
image_embed = clip_image_embeds
)
loss.backward()
# do the above for many many many steps
# now the diffusion prior can generate image embeddings from the text embeddings
Although there is the possibility they are using an unreleased, more powerful CLIP, you can use one of the released ones, if you do not wish to train your own CLIP from scratch. This will also allow the community to more quickly validate the conclusions of the paper.
To use a pretrained OpenAI CLIP, simply import OpenAIClipAdapter
and pass it into the DiffusionPrior
or Decoder
like so
import torch
from dalle2_pytorch import DALLE2, DiffusionPriorNetwork, DiffusionPrior, Unet, Decoder, OpenAIClipAdapter
# openai pretrained clip - defaults to ViT/B-32
clip = OpenAIClipAdapter()
# mock data
text = torch.randint(0, 49408, (4, 256)).cuda()
images = torch.randn(4, 3, 256, 256).cuda()
# prior networks (with transformer)
prior_network = DiffusionPriorNetwork(
dim = 512,
depth = 6,
dim_head = 64,
heads = 8
).cuda()
diffusion_prior = DiffusionPrior(
net = prior_network,
clip = clip,
timesteps = 100,
cond_drop_prob = 0.2
).cuda()
loss = diffusion_prior(text, images)
loss.backward()
# do above for many steps ...
# decoder (with unet)
unet1 = Unet(
dim = 128,
image_embed_dim = 512,
cond_dim = 128,
channels = 3,
dim_mults=(1, 2, 4, 8)
).cuda()
unet2 = Unet(
dim = 16,
image_embed_dim = 512,
cond_dim = 128,
channels = 3,
dim_mults = (1, 2, 4, 8, 16)
).cuda()
decoder = Decoder(
unet = (unet1, unet2),
image_sizes = (128, 256),
clip = clip,
timesteps = 100,
image_cond_drop_prob = 0.1,
text_cond_drop_prob = 0.5,
condition_on_text_encodings = False # set this to True if you wish to condition on text during training and sampling
).cuda()
for unet_number in (1, 2):
loss = decoder(images, unet_number = unet_number) # this can optionally be decoder(images, text) if you wish to condition on the text encodings as well, though it was hinted in the paper it didn't do much
loss.backward()
# do above for many steps
dalle2 = DALLE2(
prior = diffusion_prior,
decoder = decoder
)
images = dalle2(
['a butterfly trying to escape a tornado'],
cond_scale = 2. # classifier free guidance strength (> 1 would strengthen the condition)
)
# save your image (in this example, of size 256x256)
Now you'll just have to worry about training the Prior and the Decoder!
This repository decides to take the next step and offer DALL-E v2 combined with latent diffusion, from Rombach et al.
You can use it as follows. Latent diffusion can be limited to just the first U-Net in the cascade, or to any number you wish.
The repository also comes equipped with all the necessary settings to recreate ViT-VQGan
from the Improved VQGans paper. Furthermore, the vector quantization library also comes equipped to do residual or multi-headed quantization, which I believe will give an even further boost in performance to the autoencoder.
import torch
from dalle2_pytorch import Unet, Decoder, CLIP, VQGanVAE
# trained clip from step 1
clip = CLIP(
dim_text = 512,
dim_image = 512,
dim_latent = 512,
num_text_tokens = 49408,
text_enc_depth = 1,
text_seq_len = 256,
text_heads = 8,
visual_enc_depth = 1,
visual_image_size = 256,
visual_patch_size = 32,
visual_heads = 8
)
# 3 unets for the decoder (a la cascading DDPM)
# first two unets are doing latent diffusion
# vqgan-vae must be trained beforehand
vae1 = VQGanVAE(
dim = 32,
image_size = 256,
layers = 3,
layer_mults = (1, 2, 4)
)
vae2 = VQGanVAE(
dim = 32,
image_size = 512,
layers = 3,
layer_mults = (1, 2, 4)
)
unet1 = Unet(
dim = 32,
image_embed_dim = 512,
cond_dim = 128,
channels = 3,
sparse_attn = True,
sparse_attn_window = 2,
dim_mults = (1, 2, 4, 8)
)
unet2 = Unet(
dim = 32,
image_embed_dim = 512,
channels = 3,
dim_mults = (1, 2, 4, 8, 16),
cond_on_image_embeds = True,
cond_on_text_encodings = False
)
unet3 = Unet(
dim = 32,
image_embed_dim = 512,
channels = 3,
dim_mults = (1, 2, 4, 8, 16),
cond_on_image_embeds = True,
cond_on_text_encodings = False,
attend_at_middle = False
)
# decoder, which contains the unet(s) and clip
decoder = Decoder(
clip = clip,
vae = (vae1, vae2), # latent diffusion for unet1 (vae1) and unet2 (vae2), but not for the last unet3
unet = (unet1, unet2, unet3), # insert unets in order of low resolution to highest resolution (you can have as many stages as you want here)
image_sizes = (256, 512, 1024), # resolutions, 256 for first unet, 512 for second, 1024 for third
timesteps = 100,
image_cond_drop_prob = 0.1,
text_cond_drop_prob = 0.5
).cuda()
# mock images (get a lot of this)
images = torch.randn(1, 3, 1024, 1024).cuda()
# feed images into decoder, specifying which unet you want to train
# each unet can be trained separately, which is one of the benefits of the cascading DDPM scheme
with decoder.one_unet_in_gpu(1):
loss = decoder(images, unet_number = 1)
loss.backward()
with decoder.one_unet_in_gpu(2):
loss = decoder(images, unet_number = 2)
loss.backward()
with decoder.one_unet_in_gpu(3):
loss = decoder(images, unet_number = 3)
loss.backward()
# do the above for many steps for both unets
# then it will learn to generate images based on the CLIP image embeddings
# chaining the unets from lowest resolution to highest resolution (thus cascading)
mock_image_embed = torch.randn(1, 512).cuda()
images = decoder.sample(mock_image_embed) # (1, 3, 1024, 1024)
Training the Decoder
may be confusing, as one needs to keep track of an optimizer for each of the Unet
(s) separately. Each Unet
will also need its own corresponding exponential moving average. The DecoderTrainer
hopes to make this simple, as shown below
import torch
from dalle2_pytorch import DALLE2, Unet, Decoder, CLIP, DecoderTrainer
clip = CLIP(
dim_text = 512,
dim_image = 512,
dim_latent = 512,
num_text_tokens = 49408,
text_enc_depth = 6,
text_seq_len = 256,
text_heads = 8,
visual_enc_depth = 6,
visual_image_size = 256,
visual_patch_size = 32,
visual_heads = 8
).cuda()
# mock data
text = torch.randint(0, 49408, (4, 256)).cuda()
images = torch.randn(4, 3, 256, 256).cuda()
# decoder (with unet)
unet1 = Unet(
dim = 128,
image_embed_dim = 512,
text_embed_dim = 512,
cond_dim = 128,
channels = 3,
dim_mults=(1, 2, 4, 8)
).cuda()
unet2 = Unet(
dim = 16,
image_embed_dim = 512,
text_embed_dim = 512,
cond_dim = 128,
channels = 3,
dim_mults = (1, 2, 4, 8, 16),
cond_on_text_encodings = True
).cuda()
decoder = Decoder(
unet = (unet1, unet2),
image_sizes = (128, 256),
clip = clip,
timesteps = 1000,
condition_on_text_encodings = True
).cuda()
decoder_trainer = DecoderTrainer(
decoder,
lr = 3e-4,
wd = 1e-2,
ema_beta = 0.99,
ema_update_after_step = 1000,
ema_update_every = 10,
)
for unet_number in (1, 2):
loss = decoder_trainer(images, text = text, unet_number = unet_number) # use the decoder_trainer forward
loss.backward()
decoder_trainer.update(unet_number) # update the specific unet as well as its exponential moving average
# after much training
# you can sample from the exponentially moving averaged unets as so
mock_image_embed = torch.randn(4, 512).cuda()
images = decoder_trainer.sample(mock_image_embed, text = text) # (4, 3, 256, 256)
$ dream 'sharing a sunset at the summit of mount everest with my dog'
Once built, images will be saved to the same directory the command is invoked
- finish off gaussian diffusion class for latent embedding - allow for prediction of epsilon
- add what was proposed in the paper, where DDPM objective for image latent embedding predicts x0 directly (reread vq-diffusion paper and get caught up on that line of work)
- make sure it works end to end to produce an output tensor, taking a single gradient step
- augment unet so that it can also be conditioned on text encodings (although in paper they hinted this didn't make much a difference)
- figure out all the current bag of tricks needed to make DDPMs great (starting with the blur trick mentioned in paper)
- build the cascading ddpm by having Decoder class manage multiple unets at different resolutions
- add efficient attention in unet
- be able to finely customize what to condition on (text, image embed) for specific unet in the cascade (super resolution ddpms near the end may not need too much conditioning)
- offload unets not being trained on to CPU for memory efficiency (for training each resolution unets separately)
- build out latent diffusion architecture, with the vq-reg variant (vqgan-vae), make it completely optional and compatible with cascading ddpms
- for decoder, allow ability to customize objective (predict epsilon vs x0), in case latent diffusion does better with prediction of x0
- use attention-based upsampling https://arxiv.org/abs/2112.11435
- use inheritance just this once for sharing logic between decoder and prior network ddpms
- bring in vit-vqgan https://arxiv.org/abs/2110.04627 for the latent diffusion
- abstract interface for CLIP adapter class, so other CLIPs can be brought in
- take care of mixed precision as well as gradient accumulation within decoder trainer
- just take care of the training for the decoder in a wrapper class, as each unet in the cascade will need its own optimizer
- bring in tools to train vqgan-vae
- add convnext backbone for vqgan-vae (in addition to vit [vit-vqgan] + resnet)
- become an expert with unets, cleanup unet code, make it fully configurable, port all learnings over to https://github.com/lucidrains/x-unet
- copy the cascading ddpm code to a separate repo (perhaps https://github.com/lucidrains/denoising-diffusion-pytorch) as the main contribution of dalle2 really is just the prior network
- transcribe code to Jax, which lowers the activation energy for distributed training, given access to TPUs
- pull logic for training diffusion prior into a class DiffusionPriorTrainer, for eventual script based + CLI based training
- train on a toy task, offer in colab
- think about how best to design a declarative training config that handles preencoding for prior and training of multiple networks in decoder
- extend diffusion head to use diffusion-gan (potentially using lightweight-gan) to speed up inference
- bring in cross-scale embedding from iclr paper https://github.com/lucidrains/vit-pytorch/blob/main/vit_pytorch/crossformer.py#L14
- figure out if possible to augment with external memory, as described in https://arxiv.org/abs/2204.11824
- test out grid attention in cascading ddpm locally, decide whether to keep or remove
@misc{ramesh2022,
title = {Hierarchical Text-Conditional Image Generation with CLIP Latents},
author = {Aditya Ramesh et al},
year = {2022}
}
@misc{crowson2022,
author = {Katherine Crowson},
url = {https://twitter.com/rivershavewings}
}
@misc{rombach2021highresolution,
title = {High-Resolution Image Synthesis with Latent Diffusion Models},
author = {Robin Rombach and Andreas Blattmann and Dominik Lorenz and Patrick Esser and Björn Ommer},
year = {2021},
eprint = {2112.10752},
archivePrefix = {arXiv},
primaryClass = {cs.CV}
}
@inproceedings{Liu2022ACF,
title = {A ConvNet for the 2020s},
author = {Zhuang Liu and Hanzi Mao and Chaozheng Wu and Christoph Feichtenhofer and Trevor Darrell and Saining Xie},
year = {2022}
}
@article{shen2019efficient,
author = {Zhuoran Shen and Mingyuan Zhang and Haiyu Zhao and Shuai Yi and Hongsheng Li},
title = {Efficient Attention: Attention with Linear Complexities},
journal = {CoRR},
year = {2018},
url = {http://arxiv.org/abs/1812.01243},
}
@inproceedings{Tu2022MaxViTMV,
title = {MaxViT: Multi-Axis Vision Transformer},
author = {Zhe-Wei Tu and Hossein Talebi and Han Zhang and Feng Yang and Peyman Milanfar and Alan Conrad Bovik and Yinxiao Li},
year = {2022}
}
@article{Yu2021VectorquantizedIM,
title = {Vector-quantized Image Modeling with Improved VQGAN},
author = {Jiahui Yu and Xin Li and Jing Yu Koh and Han Zhang and Ruoming Pang and James Qin and Alexander Ku and Yuanzhong Xu and Jason Baldridge and Yonghui Wu},
journal = {ArXiv},
year = {2021},
volume = {abs/2110.04627}
}
Creating noise from data is easy; creating data from noise is generative modeling. - Yang Song's paper