ICML 2023 Papers

Diffusion models show promising generation capability for a variety of data. Despite their high generation quality, the inference for diffusion models is still time-consuming due to the numerous sampling iterations required. To accelerate the inference, we propose ReDi, a simple yet learning-free Retrieval-based Diffusion sampling framework. From a precomputed knowledge base, ReDi retrieves a trajectory similar to the partially generated trajectory at an early stage of generation, skips a large portion of intermediate steps, and continues sampling from a later step in the retrieved trajectory. We theoretically prove that the generation performance of ReDi is guaranteed. Our experiments demonstrate that ReDi improves the model inference efficiency by 2$\times$ speedup. Furthermore, ReDi is able to generalize well in zero-shot cross-domain image generation such as image stylization. The code and demo for ReDi is available at https://github.com/zkx06111/ReDiffusion.

Popular deep-learning models in the field of image classification suffer from catastrophic forgetting---models will forget previously acquired skills when learning new ones. Generative replay (GR), which typically consists of a generator and a classifier, is an efficient way to mitigate catastrophic forgetting. However, conventional GR methods only focus on a single instruction relationship (generator-to-classifier), where the generator synthesizes samples for previous tasks to instruct the training of the classifier, while ignoring the ways in which the classifier can benefit the generator. In addition, most generative replay methods typically reuse the generated samples to update the generator, which causes the samples regenerated by the generator deviating from the distribution of previous tasks. To overcome these two issues, we propose a novel approach, called deep diffusion-based generative replay (DDGR), which adopts a diffusion model as the generator and calculates an instruction-operator through the classifier to instruct the generation of samples. Extensive experiments in class incremental (CI) and class incremental with repetition (CIR) settings demonstrate the advantages of DDGR. Our code is available at https://github.com/xiaocangshengGR/DDGR.

Adversarial detection aims to determine whether a given sample is an adversarial one based on the discrepancy between natural and adversarial distributions. Unfortunately, estimating or comparing two data distributions is extremely difficult, especially in high-dimension spaces. Recently, the gradient of log probability density (a.k.a., score) w.r.t. the sample is used as an alternative statistic to compute. However, we find that the score is sensitive in identifying adversarial samples due to insufficient information with one sample only. In this paper, we propose a new statistic called expected perturbation score (EPS), which is essentially the expected score of a sample after various perturbations. Specifically, to obtain adequate information regarding one sample, we perturb it by adding various noises to capture its multi-view observations. We theoretically prove that EPS is a proper statistic to compute the discrepancy between two samples under mild conditions. In practice, we can use a pre-trained diffusion model to estimate EPS for each sample. Last, we pro- pose an EPS-based adversarial detection (EPS- AD) method, in which we develop EPS-based maximum mean discrepancy (MMD) as a metric to measure the discrepancy between the test sample and natural samples. We also prove that the EPS-based MMD between natural and adversarial samples is larger than that among natural samples. Extensive experiments show the superior adversarial detection performance of our EPS-AD.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

Text-to-image synthesis has recently seen significant progress thanks to large pretrained language models, large-scale training data, and the introduction of scalable model families such as diffusion and autoregressive models. However, the best-performing models require iterative evaluation to generate a single sample. In contrast, generative adversarial networks (GANs) only need a single forward pass. They are thus much faster, but they currently remain far behind the state-of-the-art in large-scale text-to-image synthesis. This paper aims to identify the necessary steps to regain competitiveness. Our proposed model, StyleGAN-T, addresses the specific requirements of large-scale text-to-image synthesis, such as large capacity, stable training on diverse datasets, strong text alignment, and controllable variation vs. text alignment tradeoff. StyleGAN-T significantly improves over previous GANs and outperforms distilled diffusion models - the previous state-of-the-art in fast text-to-image synthesis - in terms of sample quality and speed.

A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to ensure efficient and accurate long-distance communication between nodes, as deep convolutional networks are prone to over smoothing. In this paper, we present a novel method based on time derivative graph diffusion (TIDE) to overcome these structural limitations of the message-passing framework. Our approach allows for optimizing the spatial extent of diffusion across various tasks and network channels, thus enabling medium and long-distance communication efficiently. Furthermore, we show that our architecture design also enables local message-passing and thus inherits from the capabilities of local message-passing approaches. We show that on both widely used graph benchmarks and synthetic mesh and graph datasets, the proposed framework outperforms state-of-the-art methods by a significant margin.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs.

Designing biological sequences is an important challenge that requires satisfying complex constraints and thus is a natural problem to address with deep generative modeling. Diffusion generative models have achieved considerable success in many applications. Score-based generative stochastic differential equations (SDE) model is a continuous-time diffusion model framework that enjoys many benefits, but the originally proposed SDEs are not naturally designed for modeling discrete data. To develop generative SDE models for discrete data such as biological sequences, here we introduce a diffusion process defined in the probability simplex space with stationary distribution being the Dirichlet distribution. This makes diffusion in continuous space natural for modeling discrete data. We refer to this approach as Dirchlet diffusion score model. We demonstrate that this technique can generate samples that satisfy hard constraints using a Sudoku generation task. This generative model can also solve Sudoku, including hard puzzles, without additional training. Finally, we applied this approach to develop the first human promoter DNA sequence design model and showed that designed sequences share similar properties with natural promoter sequences.

Denoising diffusion (score-based) generative models have become a popular choice for modeling complex data. Recently, a deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been established, leading to the development of new SDE variants such as sub-VP and critically-damped Langevin. Despite the empirical success of some hand-crafted forward SDEs, many potentially promising forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing diffusion models, particularly the spatial part of forward SDEs, by leveraging the symplectic and Riemannian geometry of the data manifold. We introduce a systematic formalism with theoretical guarantees and connect it with previous diffusion models. Finally, we demonstrate the theoretical advantages of our method from a variational optimization perspective. We present numerical experiments on synthetic datasets, MNIST and CIFAR10 to validate the effectiveness of our framework.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

Attention-based vision models, such as Vision Transformer (ViT) and its variants, have shown promising performance in various computer vision tasks. However, these emerging architectures suffer from large model sizes and high computational costs, calling for efficient model compression solutions. To date, pruning ViTs has been well studied, while other compression strategies that have been widely applied in CNN compression, e.g., model factorization, is little explored in the context of ViT compression. This paper explores an efficient method for compressing vision transformers to enrich the toolset for obtaining compact attention-based vision models. Based on the new insight on the multi-head attention layer, we develop a highly efficient ViT compression solution, which outperforms the state-of-the-art pruning methods. For compressing DeiT-small and DeiT-base models on ImageNet, our proposed approach can achieve $0.45\%$ and $0.76\%$ higher top-1 accuracy even with fewer parameters. Our finding can also be applied to improve the customization efficiency of text-to-image diffusion models, with much faster training (up to $2.6\times$ speedup) and lower extra storage cost (up to $1927.5\times$ reduction) than the existing works.

Graph neural networks (GNNs) are one of the most popular research topics for deep learning. GNN methods typically have been designed on top of the graph signal processing theory. In particular, diffusion equations have been widely used for designing the core processing layer of GNNs, and therefore they are inevitably vulnerable to the notorious oversmoothing problem. Recently, a couple of papers paid attention to reaction equations in conjunctions with diffusion equations. However, they all consider limited forms of reaction equations. To this end, we present a reaction-diffusion equation-based GNN method that considers all popular types of reaction equations in addition to one special reaction equation designed by us. To our knowledge, our paper is one of the most comprehensive studies on reaction-diffusion equation-based GNNs. In our experiments with 9 datasets and 28 baselines, our method, called GREAD, outperforms them in a majority of cases. Further synthetic data experiments show that it mitigates the oversmoothing problem and works well for various homophily rates.

Diffusion-based methods, represented as stochastic differential equations on a continuous-time domain, have recently proven successful as non-adversarial generative models. Training such models relies on denoising score matching, which can be seen as multi-scale denoising autoencoders. Here, we augment the denoising score matching framework to enable representation learning without any supervised signal. GANs and VAEs learn representations by directly transforming latent codes to data samples. In contrast, the introduced diffusion-based representation learning relies on a new formulation of the denoising score matching objective and thus encodes the information needed for denoising. We illustrate how this difference allows for manual control of the level of details encoded in the representation. Using the same approach, we propose to learn an infinite-dimensional latent code that achieves improvements on state-of-the-art models on semi-supervised image classification. We also compare the quality of learned representations of diffusion score matching with other methods like autoencoder and contrastively trained systems through their performances on downstream tasks. Finally, we also ablate with a different SDE formulation for diffusion models and show that the benefits on downstream tasks are still present on changing the underlying differential equation.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Further, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on subspace dimension, implying that diffusion models can circumvent the curse of data ambient dimensionality.

The proposed method, **Discriminator Guidance**, aims to improve sample generation of pre-trained diffusion models. The approach introduces a discriminator that gives explicit supervision to a denoising sample path whether it is realistic or not. Unlike GANs, our approach does not require joint training of score and discriminator networks. Instead, we train the discriminator after score training, making discriminator training stable and fast to converge. In sample generation, we add an auxiliary term to the pre-trained score to deceive the discriminator. This term corrects the model score to the data score at the optimal discriminator, which implies that the discriminator helps better score estimation in a complementary way. Using our algorithm, we achive state-of-the-art results on ImageNet 256x256 with FID 1.83 and recall 0.64, similar to the validation data's FID (1.68) and recall (0.66). We release the code at https://github.com/alsdudrla10/DG.

We consider guiding denoising diffusion models with general differentiable loss functions in a plug-and-play fashion, enabling controllable generation without additional training. This paradigm, termed Loss-Guided Diffusion (LGD), can easily be integrated into all diffusion models and leverage various efficient samplers. Despite the benefits, the resulting guidance term is, unfortunately, an intractable integral and needs to be approximated. Existing methods compute the guidance term based on a point estimate. However, we show that such approaches have significant errors over the scale of the approximations. To address this issue, we propose a Monte Carlo method that uses multiple samples from a suitable distribution to reduce bias. Our method is effective in various synthetic and real-world settings, including image super-resolution, text or label-conditional image generation, and controllable motion synthesis. Notably, we show how our method can be applied to control a pretrained motion diffusion model to follow certain paths and avoid obstacles that are proven challenging to prior methods.