Purify++: Improving Diffusion-Purification with Advanced Diffusion Models and Control of Randomness

Adversarial attacks can mislead neural network classifiers. The defense against adversarial attacks is important for AI safety. Adversarial purification is a family of approaches that defend adversarial attacks with suitable pre-processing. Diffusion models have been shown to be effective for adversarial purification. Despite their success, many aspects of diffusion purification still remain unexplored. In this paper, we investigate and improve upon three limiting designs of diffusion purification: the use of an improved diffusion model, advanced numerical simulation techniques, and optimal control of randomness. Based on our findings, we propose Purify++, a new diffusion purification algorithm that is now the state-of-the-art purification method against several adversarial attacks. Our work presents a systematic exploration of the limits of diffusion purification methods.

SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. The majority of such techniques consider solving the diffusion ODE due to its superior efficiency. However, stochastic sampling could offer additional advantages in generating diverse and high-quality data. In this work, we engage in a comprehensive analysis of stochastic sampling from two aspects: variance-controlled diffusion SDE and linear multi-step SDE solver. Based on our analysis, we propose SA-Solver, which is an improved efficient stochastic Adams method for solving diffusion SDE to generate data with high quality. Our experiments show that SA-Solver achieves: 1) improved or comparable performance compared with the existing state-of-the-art sampling methods for few-step sampling; 2) SOTA FID scores on substantial benchmark datasets under a suitable number of function evaluations (NFEs).

Enhancing Adversarial Robustness via Score-Based Optimization

Adversarial attacks have the potential to mislead deep neural network classifiers by introducing slight perturbations. Developing algorithms that can mitigate the effects of these attacks is crucial for ensuring the safe use of artificial intelligence. Recent studies have suggested that score-based diffusion models are effective in adversarial defenses. However, existing diffusion-based defenses rely on the sequential simulation of the reversed stochastic differential equations of diffusion models, which are computationally inefficient and yield suboptimal results. In this paper, we introduce a novel adversarial defense scheme named ScoreOpt, which optimizes adversarial samples at test-time, towards original clean data in the direction guided by score-based priors. We conduct comprehensive experiments on multiple datasets, including CIFAR10, CIFAR100 and ImageNet. Our experimental results demonstrate that our approach outperforms existing adversarial defenses in terms of both robustness performance and inference speed.

Training Energy-Based Models with Diffusion Contrastive Divergences

Energy-Based Models (EBMs) have been widely used for generative modeling. Contrastive Divergence (CD), a prevailing training objective for EBMs, requires sampling from the EBM with Markov Chain Monte Carlo methods (MCMCs), which leads to an irreconcilable trade-off between the computational burden and the validity of the CD. Running MCMCs till convergence is computationally intensive. On the other hand, short-run MCMC brings in an extra non-negligible parameter gradient term that is difficult to handle. In this paper, we provide a general interpretation of CD, viewing it as a special instance of our proposed Diffusion Contrastive Divergence (DCD) family. By replacing the Langevin dynamic used in CD with other EBM-parameter-free diffusion processes, we propose a more efficient divergence. We show that the proposed DCDs are both more computationally efficient than the CD and are not limited to a non-negligible gradient term. We conduct intensive experiments, including both synthesis data modeling and high-dimensional image denoising and generation, to show the advantages of the proposed DCDs. On the synthetic data learning and image denoising experiments, our proposed DCD outperforms CD by a large margin. In image generation experiments, the proposed DCD is capable of training an energy-based model for generating the Celab-A $32\times 32$ dataset, which is comparable to existing EBMs.

Entropy-based Training Methods for Scalable Neural Implicit Sampler

Efficiently sampling from un-normalized target distributions is a fundamental problem in scientific computing and machine learning. Traditional approaches like Markov Chain Monte Carlo (MCMC) guarantee asymptotically unbiased samples from such distributions but suffer from computational inefficiency, particularly when dealing with high-dimensional targets, as they require numerous iterations to generate a batch of samples. In this paper, we propose an efficient and scalable neural implicit sampler that overcomes these limitations. Our sampler can generate large batches of samples with low computational costs by leveraging a neural transformation that directly maps easily sampled latent vectors to target samples without the need for iterative procedures. To train the neural implicit sampler, we introduce two novel methods: the KL training method and the Fisher training method. The former minimizes the Kullback-Leibler divergence, while the latter minimizes the Fisher divergence. By employing these training methods, we effectively optimize the neural implicit sampler to capture the desired target distribution. To demonstrate the effectiveness, efficiency, and scalability of our proposed samplers, we evaluate them on three sampling benchmarks with different scales. These benchmarks include sampling from 2D targets, Bayesian inference, and sampling from high-dimensional energy-based models (EBMs). Notably, in the experiment involving high-dimensional EBMs, our sampler produces samples that are comparable to those generated by MCMC-based methods while being more than 100 times more efficient, showcasing the efficiency of our neural sampler. We believe that the theoretical and empirical contributions presented in this work will stimulate further research on developing efficient samplers for various applications beyond the ones explored in this study.

Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models

Due to the ease of training, ability to scale, and high sample quality, diffusion models (DMs) have become the preferred option for generative modeling, with numerous pre-trained models available for a wide variety of datasets. Containing intricate information about data distributions, pre-trained DMs are valuable assets for downstream applications. In this work, we consider learning from pre-trained DMs and transferring their knowledge to other generative models in a data-free fashion. Specifically, we propose a general framework called Diff-Instruct to instruct the training of arbitrary generative models as long as the generated samples are differentiable with respect to the model parameters. Our proposed Diff-Instruct is built on a rigorous mathematical foundation where the instruction process directly corresponds to minimizing a novel divergence we call Integral Kullback-Leibler (IKL) divergence. IKL is tailored for DMs by calculating the integral of the KL divergence along a diffusion process, which we show to be more robust in comparing distributions with misaligned supports. We also reveal non-trivial connections of our method to existing works such as DreamFusion, and generative adversarial training. To demonstrate the effectiveness and universality of Diff-Instruct, we consider two scenarios: distilling pre-trained diffusion models and refining existing GAN models. The experiments on distilling pre-trained diffusion models show that Diff-Instruct results in state-of-the-art single-step diffusion-based models. The experiments on refining GAN models show that the Diff-Instruct can consistently improve the pre-trained generators of GAN models across various settings.

A Comprehensive Survey on Knowledge Distillation of Diffusion Models

Diffusion Models (DMs), also referred to as score-based diffusion models, utilize neural networks to specify score functions. Unlike most other probabilistic models, DMs directly model the score functions, which makes them more flexible to parametrize and potentially highly expressive for probabilistic modeling. DMs can learn fine-grained knowledge, i.e., marginal score functions, of the underlying distribution. Therefore, a crucial research direction is to explore how to distill the knowledge of DMs and fully utilize their potential. Our objective is to provide a comprehensible overview of the modern approaches for distilling DMs, starting with an introduction to DMs and a discussion of the challenges involved in distilling them into neural vector fields. We also provide an overview of the existing works on distilling DMs into both stochastic and deterministic implicit generators. Finally, we review the accelerated diffusion sampling algorithms as a training-free method for distillation. Our tutorial is intended for individuals with a basic understanding of generative models who wish to apply DM's distillation or embark on a research project in this field.

A Lipschitz Bandits Approach for Continuous Hyperparameter Optimization

One of the most critical problems in machine learning is HyperParameter Optimization (HPO), since choice of hyperparameters has a significant impact on final model performance. Although there are many HPO algorithms, they either have no theoretical guarantees or require strong assumptions. To this end, we introduce BLiE -- a Lipschitz-bandit-based algorithm for HPO that only assumes Lipschitz continuity of the objective function. BLiE exploits the landscape of the objective function to adaptively search over the hyperparameter space. Theoretically, we show that $(i)$ BLiE finds an $\epsilon$-optimal hyperparameter with $O \left( \frac{1}{\epsilon} \right)^{d_z + \beta}$ total budgets, where $d_z$ and $\beta$ are problem intrinsic; $(ii)$ BLiE is highly parallelizable. Empirically, we demonstrate that BLiE outperforms the state-of-the-art HPO algorithms on benchmark tasks. We also apply BLiE to search for noise schedule of diffusion models. Comparison with the default schedule shows that BLiE schedule greatly improves the sampling speed.

ABM: an automatic supervised feature engineering method for loss based models based on group and fused lasso

A vital problem in solving classification or regression problem is to apply feature engineering and variable selection on data before fed into models.One of a most popular feature engineering method is to discretisize continous variable with some cutting points,which is refered to as bining processing.Good cutting points are important for improving model's ability, because wonderful bining may ignore some noisy variance in continous variable range and keep useful leveled information with good ordered encodings.However, to our best knowledge a majority of cutting point selection is done via researchers domain knownledge or some naive methods like equal-width cutting or equal-frequency cutting.In this paper we propose an end-to-end supervised cutting point selection method based on group and fused lasso along with the automatically variable selection effect.We name our method \textbf{ABM}(automatic bining machine). We firstly cut each variable range into fine grid bins and train model with our group and group fused lasso regularization on each successive bins.It is a method that integrates feature engineering,variable selection and model training simultanously.And one more inspiring thing is that the method is flexible such that it can be taken into a bunch of loss function based model including deep neural networks.We have also implemented the method in R and open the source code to other researchers.A Python version will also meet the community in days.