Tim Salimans
Tim is a Machine Learning research scientist working on generative modeling. He is well known for his work on GANs and VAEs, and their evaluation using the Inception score, as well as his work on autoregressive generative models like GPT-1 and PixelCNN++. More recently, he has been focusing on diffusion models for generating images (Imagen) and video (Imagen Video), and on making these models fast to sample using distillation.
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This paper studies non-autoregressive transformers for the image synthesis task from the lens of discrete diffusion models. We find that generative methods based on non-autoregressive transformers suffer from decoding compounding error due to the parallel sampling of visual tokens. To alleviate it, we introduce discrete predictor-corrector diffusion models (DPC). Predictor-corrector samplers are a recently introduced class of samplers for diffusion models which improve upon ancestral samplers by correcting the sampling distribution of intermediate diffusion states using MCMC methods. In DPC, the Langevin corrector, which does not have a direct counterpart in discrete space, is replaced with a discrete MCMC transition defined by a learned corrector kernel. The corrector kernel is trained to make the correction steps achieve asymptotic convergence, in distribution, to the real marginal of the intermediate diffusion states. Our experiments show that equipped with DPC, discrete diffusion models can achieve comparable quality to continuous diffusion models, while having orders of magnitude faster sampling times. DPC improves upon existing discrete latent space models for class-conditional image generation on ImageNet, and outperforms recent diffusion models and GANs, according to visual evaluation user studies.
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Palette: Image-to-Image Diffusion Models
Chitwan Saharia
Chris A. Lee
Huiwen Chang
Jonathan Ho
Mohammad Norouzi
William Chan
SIGGRAPH 2022(2022)
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This paper develops a unified framework for image-to-image translation based on conditional diffusion models and evaluates this framework on four challenging image-to-image translation tasks, namely colorization, inpainting, uncropping, and JPEG restoration. Our simple implementation of image-to-image diffusion models outperforms strong GAN and regression baselines on all tasks, without task-specific hyper-parameter tuning, architecture customization, or any auxiliary loss or sophisticated new techniques needed. We uncover the impact of an L2 vs. L1 loss in the denoising diffusion objective on sample diversity, and demonstrate the importance of self-attention in the neural architecture through empirical studies. Importantly, we advocate a unified evaluation protocol based on ImageNet, with human evaluation and sample quality scores (FID, Inception Score, Classification Accuracy of a pre-trained ResNet-50, and Perceptual Distance against original images). We expect this standardized evaluation protocol to play a role in advancing image-to-image translation research. Finally, we show that a generalist, multi-task diffusion model performs as well or better than task-specific specialist counterparts. Check out https://diffusion-palette.github.io/ for an overview of the results.
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Cascaded Diffusion Models for High Fidelity Image Generation
Jonathan Ho
Chitwan Saharia
William Chan
Mohammad Norouzi
https://cascaded-diffusion.github.io/(2021)
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We show that cascaded diffusion models are capable of generating high fidelity images on the class-conditional ImageNet generation challenge, without any assistance from auxiliary image classifiers to boost sample quality. A cascaded diffusion model comprises a pipeline of multiple diffusion models that generate images of increasing resolution, beginning with a standard diffusion model at the lowest resolution, followed by one or more super-resolution diffusion models that successively upsample the image and add higher resolution details. We find that the sample quality of a cascading pipeline relies crucially on conditioning augmentation, our proposed method of data augmentation of the lower resolution conditioning inputs to the super-resolution models. Our experiments show that conditioning augmentation prevents compounding error during sampling in a cascaded model, helping us to train cascading pipelines achieving FID scores of 1.48 at 64x64, 3.52 at 128x128 and 4.88 at 256x256 resolutions, outperforming BigGAN-deep, and classification accuracy scores of 63.02% (top-1) and 84.06% (top-5) at 256x256, outperforming VQ-VAE-2.
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Variational Diffusion Models
Diederik P. Kingma
Ben Poole
Jonathan Ho
Advances in Neural Information Processing Systems 34 (NeurIPS 2021)(2021)
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Diffusion-based generative models have demonstrated a capacity for perceptually impressive synthesis, but can they also be great likelihood-based models? We answer this in the affirmative, and introduce a family of diffusion-based generative models that obtain state-of-the-art likelihoods on standard image density estimation benchmarks. Unlike other diffusion-based models, our method allows for efficient optimization of the noise schedule jointly with the rest of the model. We show that the variational lower bound (VLB) simplifies to a remarkably short expression in terms of the signal-to-noise ratio of the diffused data, thereby improving our theoretical understanding of this model class. Using this insight, we prove an equivalence between several models proposed in the literature. In addition, we show that the continuous-time VLB is invariant to the noise schedule, except for the signal-to-noise ratio at its endpoints. This enables us to learn a noise schedule that minimizes the variance of the resulting VLB estimator, leading to faster optimization. Combining these advances with architectural improvements, we obtain state-of-the-art likelihoods on image density estimation benchmarks, outperforming autoregressive models that have dominated these benchmarks for many years, with often significantly faster optimization. In addition, we show how to use the model as part of a bits-back compression scheme, and demonstrate lossless compression rates close to the theoretical optimum.
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IDF++: Analyzing and Improving Integer Discrete Flows for Lossless Compression
Rianne van den Berg
Casper Kaae Sønderby
ICLR 2021, ICLR 2021 (to appear)
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In this paper we analyse and improve integer discrete flows for lossless compression. Integer discrete flows are a recently proposed class of models that learn invertible transformations for integer-valued random variables. Their discrete nature makes them particularly suitable for lossless compression with entropy coding schemes. We start by investigating a recent theoretical claim that states that invertible flows for discrete random variables are less flexible than their continuous counterparts. We demonstrate with a proof that this claim does not hold for integer discrete flows due to the embedding of data with finite support into the countably infinite integer lattice. Furthermore, we zoom in on the effect of gradient bias due to the straight-through estimator in integer discrete flows, and demonstrate that its influence is highly dependent on architecture choices and less prominent than previously thought. Finally, we show how different modifications to the architecture improve the performance of this model class for lossless compression.
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Image Super-Resolution via Iterative Refinement
Chitwan Saharia
Jonathan Ho
Mohammad Norouzi
William Chan
Submission to ICCV 2021
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We present SR3, an approach to image Super-Resolution via Repeated Refinement. SR3 adapts denoising diffusion probabilistic models to conditional image generation and performs super-resolution through a stochastic denoising process. Inference starts with pure Gaussian noise and iteratively refines the noisy output using a U-Net model trained on denoising at various noise levels. SR3 exhibits
strong performance on super-resolution tasks at different magnification factors, on faces and natural images. We conduct human evaluation on a standard 8× face super-resolution task on CelebA-HQ, comparing with SOTA GAN methods. SR3 achieves a fool rate close to 50%, suggesting
photo-realistic outputs, while GAN baselines do not exceed a fool rate of 34%. We further show the effectiveness of SR3 in cascaded image generation, where generative models are chained with super-resolution models, yielding competitive FID scores on ImageNet.
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A Spectral Energy Distance for Parallel Speech Synthesis
Jasper Roland Snoek
Rianne van den Berg
(2020)
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Speech synthesis is an important practical generative modeling problem that has seen great progress over the last few years, with likelihood-based autoregressive neural models now outperforming traditional concatenative systems. A downside of such autoregressive models is that they require executing tens of thousands of sequential operations per second of generated audio, making them ill-suited for deployment on specialized deep learning hardware. Here, we propose a new learning method that allows us to train highly parallel models of speech, without requiring access to an analytical likelihood function. Our approach is based on a generalized energy distance between the distributions of the generated and real audio. This spectral energy distance is a proper scoring rule with respect to the distribution over magnitude-spectrograms of the generated waveform audio and offers statistical consistency guarantees. The distance can be calculated from minibatches without bias, and does not involve adversarial learning, yielding a stable and consistent method for training implicit generative models. Empirically, we achieve state-of-the-art generation quality among implicit generative models, as judged by the recently proposed cFDSD metric. When combining our method with adversarial techniques, we also improve upon the recently proposed GAN-TTS model in terms of Mean Opinion Score as judged by trained human evaluators.
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MetNet: A Neural Weather Model for Precipitation Forecasting
Casper Kaae Sønderby
Avital Oliver
Jason Hickey
Submission to journal(2020)
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Weather forecasting is a long standing scientific challenge with direct social and economic impact. The task is suitable for deep neural networks due to vast amounts of continuously collected data and a rich spatial and temporal structure that presents long range dependencies. We introduce MetNet, a neural network that forecasts precipitation up to 8 hours into the future at the high spatial resolution of 1 km and at the temporal resolution of 2 minutes with a latency in the order of seconds. MetNet takes as input radar and satellite data and forecast lead time and produces a probabilistic precipitation map. The architecture uses axial self-attention to aggregate the global context from a large input patch corresponding to a million square kilometers. We evaluate the performance of MetNet at various precipitation thresholds and find that MetNet outperforms Numerical Weather Prediction at forecasts of up to 7 to 8 hours on the scale of the continental United States.
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PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications
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PixelCNNs are a recently proposed class of powerful generative models with tractable likelihood. Here we discuss our implementation of PixelCNNs which we make available at https://github.com/openai/pixel-cnn. Our implementation contains a number of modifications to the original model that both simplify its structure and improve its performance. 1) We use a discretized logistic mixture likelihood on the pixels, rather than a 256-way softmax, which we find to speed up training. 2) We condition on whole pixels, rather than R/G/B sub-pixels, simplifying the model structure. 3) We use downsampling to efficiently capture structure at multiple resolutions. 4) We introduce additional short-cut connections to further speed up optimization. 5) We regularize the model using dropout. Finally, we present state-of-the-art log likelihood results on CIFAR-10 to demonstrate the usefulness of these modifications.
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Improved Variational Inference with Inverse Autoregressive Flow
Diederik P. Kingma
Rafal Jozefowicz
Xi Chen
Ilya Sutskever
Max Welling
Proceedings of NIPS'16(2016)
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The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed flow consists of a chain of invertible transformations, where each transformation is based on an autoregressive neural network. In experiments, we show that IAF significantly improves upon diagonal Gaussian approximate posteriors. In addition, we demonstrate that a novel type of variational autoencoder, coupled with IAF, is competitive with neural autoregressive models in terms of attained log-likelihood on natural images, while allowing significantly faster synthesis.
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Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks
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We present weight normalization: a reparameterization of the weight vectors in a neural network that decouples the length of those weight vectors from their direction. By reparameterizing the weights in this way we improve the conditioning of the optimization problem and we speed up convergence of stochastic gradient descent. Our reparameterization is inspired by batch normalization but does not introduce any dependencies between the examples in a minibatch. This means that our method can also be applied successfully to recurrent models such as LSTMs and to noise-sensitive applications such as deep reinforcement learning or generative models, for which batch normalization is less well suited. Although our method is much simpler, it still provides much of the speed-up of full batch normalization. In addition, the computational overhead of our method is lower, permitting more optimization steps to be taken in the same amount of time. We demonstrate the usefulness of our method on applications in supervised image recognition, generative modelling, and deep reinforcement learning.
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Variational Dropout and the Local Reparameterization Trick
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We explore an as yet unexploited opportunity for drastically improving the efficiency of stochastic gradient variational Bayes (SGVB) with global model parameters. Regular SGVB estimators rely on sampling of parameters once per minibatch of data, and have variance that is constant wrt the minibatch size. The efficiency of such estimators can be drastically improved upon by translating uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such reparameterizations with local noise can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. We find an important connection with regularization by dropout: the original Gaussian dropout objective corresponds to SGVB with local noise, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose\emph {variational dropout}, a generalization of Gaussian dropout, but with a more flexibly parameterized posterior, often leading to better generalization. The method is demonstrated through several experiments.
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Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
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Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation. By doing so we obtain a rich class of inference algorithms bridging the gap between variational methods and MCMC, and offering the best of both worlds: fast posterior approximation through the maximization of an explicit objective, with the option of trading off additional computation for additional accuracy. We describe the theoretical foundations that make this possible and show some promising first results.
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