Diffusion Probabilistic Models (DPMs) have achieved significant success in generative tasks. However, their training and sampling processes suffer from the issue of distribution mismatch. During the denoising process, the input data distributions differ between the training and inference stages, potentially leading to inaccurate data generation. To obviate this, we analyze the training objective of DPMs and theoretically demonstrate that this mismatch can be alleviated through Distributionally Robust Optimization (DRO), which is equivalent to performing robustness-driven Adversarial Training (AT) on DPMs. Furthermore, for the recently proposed Consistency Model (CM), which distills the inference process of the DPM, we prove that its training objective also encounters the mismatch issue. Fortunately, this issue can be mitigated by AT as well. Based on these insights, we propose to conduct efficient AT on both DPM and CM. Finally, extensive empirical studies validate the effectiveness of AT in diffusion-based models. The code is available at https://github.com/kugwzk/AT_Diff.

The capabilities of large language models (LLMs) significantly depend on training data drawn from various domains. Optimizing domain-specific mixture ratios can be modeled as a bi-level optimization problem, which we simplify into a single-level penalized form and solve with twin networks: a proxy model trained on primary data and a dynamically updated reference model trained with additional data. Our proposed method, Twin Networks for bi-level DatA mixturE optiMization (TANDEM), measures the data efficacy through the difference between the twin models and up-weights domains that benefit more from the additional data. TANDEM provides theoretical guarantees and wider applicability, compared to prior approaches. Furthermore, our bi-level perspective suggests new settings to study domain reweighting such as data-restricted scenarios and supervised fine-tuning, where optimized mixture ratios significantly improve the performance. Extensive experiments validate TANDEM's effectiveness in all scenarios.

Recently, optimization on the Riemannian manifold have provided valuable insights to the optimization community. In this regard, extending these methods to to the Wasserstein space is of particular interest, since optimization on Wasserstein space is closely connected to practical sampling processes. Generally, the standard (continuous) optimization method on Wasserstein space is Riemannian gradient flow (i.e., Langevin dynamics when minimizing KL divergence). In this paper, we aim to enrich the family of continuous optimization methods in the Wasserstein space, by extending the gradient flow on it into the stochastic gradient descent (SGD) flow and stochastic variance reduction gradient (SVRG) flow. By leveraging the property of Wasserstein space, we construct stochastic differential equations (SDEs) to approximate the corresponding discrete Euclidean dynamics of the desired Riemannian stochastic methods. Then, we obtain the flows in Wasserstein space by Fokker-Planck equation. Finally, we establish convergence rates of the proposed stochastic flows, which align with those known in the Euclidean setting.

Parameter-efficient transfer learning (PETL) methods show promise in adapting a pre-trained model to various downstream tasks while training only a few parameters. In the computer vision (CV) domain, numerous PETL algorithms have been proposed, but their direct employment or comparison remains inconvenient. To address this challenge, we construct a Unified Visual PETL Benchmark (V-PETL Bench) for the CV domain by selecting 30 diverse, challenging, and comprehensive datasets from image recognition, video action recognition, and dense prediction tasks. On these datasets, we systematically evaluate 25 dominant PETL algorithms and open-source a modular and extensible codebase for fair evaluation of these algorithms. V-PETL Bench runs on NVIDIA A800 GPUs and requires approximately 310 GPU days. We release all the benchmark, making it more efficient and friendly to researchers. Additionally, V-PETL Bench will be continuously updated for new PETL algorithms and CV tasks.

Recently, the strong latent Diffusion Probabilistic Model (DPM) has been applied to high-quality Text-to-Image (T2I) generation (e.g., Stable Diffusion), by injecting the encoded target text prompt into the gradually denoised diffusion image generator. Despite the success of DPM in practice, the mechanism behind it remains to be explored. To fill this blank, we begin by examining the intermediate statuses during the gradual denoising generation process in DPM. The empirical observations indicate, the shape of image is reconstructed after the first few denoising steps, and then the image is filled with details (e.g., texture). The phenomenon is because the low-frequency signal (shape relevant) of the noisy image is not corrupted until the final stage in the forward process (initial stage of generation) of adding noise in DPM. Inspired by the observations, we proceed to explore the influence of each token in the text prompt during the two stages. After a series of experiments of T2I generations conditioned on a set of text prompts. We conclude that in the earlier generation stage, the image is mostly decided by the special token [\texttt{EOS}] in the text prompt, and the information in the text prompt is already conveyed in this stage. After that, the diffusion model completes the details of generated images by information from themselves. Finally, we propose to apply this observation to accelerate the process of T2I generation by properly removing text guidance, which finally accelerates the sampling up to 25\%+.

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 (SOTA) sampling methods for few-step sampling; 2) SOTA FID on substantial benchmark datasets under a suitable number of function evaluations (NFEs).

In real-world applications, it is important and desirable to learn a model that performs well on out-of-distribution (OOD) data. Recently, causality has become a powerful tool to tackle the OOD generalization problem, with the idea resting on the causal mechanism that is invariant across domains of interest. To leverage the generally unknown causal mechanism, existing works assume a linear form of causal feature or require sufficiently many and diverse training domains, which are usually restrictive in practice. In this work, we obviate these assumptions and tackle the OOD problem without explicitly recovering the causal feature. Our approach is based on transformations that modify the non-causal feature but leave the causal part unchanged, which can be either obtained from prior knowledge or learned from the training data in the multi-domain scenario. Under the setting of invariant causal mechanism, we theoretically show that if all such transformations are available, then we can learn a minimax optimal model across the domains using only single domain data. Noticing that knowing a complete set of these causal invariant transformations may be impractical, we further show that it suffices to know only a subset of these transformations. Based on the theoretical findings, a regularized training procedure is proposed to improve the OOD generalization capability. Extensive experimental results on both synthetic and real datasets verify the effectiveness of the proposed algorithm, even with only a few causal invariant transformations.

We establish upper bounds for the expected excess risk of models trained by proper iterative algorithms which approximate the local minima. Unlike the results built upon the strong globally strongly convexity or global growth conditions e.g., PL-inequality, we only require the population risk to be \emph{locally} strongly convex around its local minima. Concretely, our bound under convex problems is of order $\tilde{\mathcal{O}}(1/n)$. For non-convex problems with $d$ model parameters such that $d/n$ is smaller than a threshold independent of $n$, the order of $\tilde{\mathcal{O}}(1/n)$ can be maintained if the empirical risk has no spurious local minima with high probability. Moreover, the bound for non-convex problem becomes $\tilde{\mathcal{O}}(1/\sqrt{n})$ without such assumption. Our results are derived via algorithmic stability and characterization of the empirical risk's landscape. Compared with the existing algorithmic stability based results, our bounds are dimensional insensitive and without restrictions on the algorithm's implementation, learning rate, and the number of iterations. Our bounds underscore that with locally strongly convex population risk, the models trained by any proper iterative algorithm can generalize well, even for non-convex problems, and $d$ is large.

Batch normalization (BN) has become a critical component across diverse deep neural networks. The network with BN is invariant to positively linear re-scale transformation, which makes there exist infinite functionally equivalent networks with different scales of weights. However, optimizing these equivalent networks with the first-order method such as stochastic gradient descent will obtain a series of iterates converging to different local optima owing to their different gradients across training. To obviate this, we propose a quotient manifold PSI manifold, in which all the equivalent weights of the network with BN are regarded as the same element. Next, we construct gradient descent and stochastic gradient descent on the proposed PSI manifold to train the network with BN. The two algorithms guarantee that every group of equivalent weights (caused by positively re-scaling) converge to the equivalent optima. Besides that, we give convergence rates of the proposed algorithms on the PSI manifold. The results show that our methods accelerate training compared with the algorithms on the Euclidean weight space. Finally, empirical results verify that our algorithms consistently improve the existing methods in both convergence rate and generalization ability under various experimental settings.

Recently, learning a model that generalizes well on out-of-distribution (OOD) data has attracted great attention in the machine learning community. In this paper, after defining OOD generalization by Wasserstein distance, we theoretically justify that a model robust to input perturbation also generalizes well on OOD data. Inspired by previous findings that adversarial training helps improve robustness, we show that models trained by adversarial training have converged excess risk on OOD data. Besides, in the paradigm of pre-training then fine-tuning, we theoretically justify that the input perturbation robust model in the pre-training stage provides an initialization that generalizes well on downstream OOD data. Finally, various experiments conducted on image classification and natural language understanding tasks verify our theoretical findings.

It is arguably believed that flatter minima can generalize better. However, it has been pointed out that the usual definitions of sharpness, which consider either the maxima or the integral of loss over a delta ball of parameters around minima, cannot give consistent measurement for scale invariant neural networks, e.g., networks with batch normalization layer. In this paper, we first propose a measure of sharpness, BN-Sharpness, which gives consistent value for equivalent networks under BN. It achieves the property of scale invariance by connecting the integral diameter with the scale of parameter. Then we present a computation-efficient way to calculate the BN-sharpness approximately i.e., one dimensional integral along the "sharpest" direction. Furthermore, we use the BN-sharpness to regularize the training and design an algorithm to minimize the new regularized objective. Our algorithm achieves considerably better performance than vanilla SGD over various experiment settings.