Statistically, we study the universal approximation and sample complexity of the DiTs score function, as well as the distribution recovery property of the initial data. Specifically, under mild data assumptions, we derive an approximation error bound for the score network of latent DiTs, which is sub-linear in the latent space dimension. Additionally, we derive the corresponding sample complexity bound and show that the data distribution generated from the estimated score function converges toward a proximate area of the original one.Computationally, we characterize the hardness of both forward inference and backward computation of latent DiTs, assuming the Strong Exponential Time Hypothesis (SETH). For forward inference, we identify efficient criteria for all possible latent DiTs inference algorithms and showcase our theory by pushing the efficiency toward almost-linear time inference.

How do AI models generate videos? With powerful video generation tools now in the hands of more people than ever, let's take a look at how they work. It's been a big year for video generation. In the last nine months OpenAI made Sora public, Google DeepMind launched Veo 3, the video startup Runway launched Gen-4. All can produce video clips that are (almost) impossible to distinguish from actual filmed footage or CGI animation. This year also saw Netflix debut an AI visual effect in its show, the first time video generation has been used to make mass-market TV.

Generating high-quality 3D assets from text and images has long been challenging, primarily due to the absence of scalable 3D representations capable of capturing intricate geometry distributions. In this work, we introduce Direct3D, a native 3D generative model scalable to in-the-wild input images, without requiring a multi-view diffusion model or SDS optimization. Our approach comprises two primary components: a Direct 3D Variational Auto-Encoder (D3D-VAE) and a Direct 3D Diffusion Transformer (D3D-DiT). D3D-VAE efficiently encodes high-resolution 3D shapes into a compact and continuous latent triplane space. Notably, our method directly supervises the decoded geometry using a semi-continuous surface sampling strategy, diverging from previous methods relying on rendered images as supervision signals.

We investigate the statistical and computational limits of latent Diffusion Transformers (DiTs) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs score function, as well as the distribution recovery property of the initial data. Specifically, under mild data assumptions, we derive an approximation error bound for the score network of latent DiTs, which is sub-linear in the latent space dimension. Additionally, we derive the corresponding sample complexity bound and show that the data distribution generated from the estimated score function converges toward a proximate area of the original one.Computationally, we characterize the hardness of both forward inference and backward computation of latent DiTs, assuming the Strong Exponential Time Hypothesis (SETH). For forward inference, we identify efficient criteria for all possible latent DiTs inference algorithms and showcase our theory by pushing the efficiency toward almost-linear time inference.

In this paper, we propose a diffusion model that integrates a representation-conditioning mechanism, where the representations derived from a Vision Transformer (ViT) are used to condition the internal process of a Transformer-based diffusion model. This approach enables representation-conditioned data generation, addressing the challenge of requiring large-scale labeled datasets by leveraging self-supervised learning on unlabeled data. We evaluate our method through a zero-shot classification task for hematoma detection in brain imaging. Compared to the strong contrastive learning baseline, DINOv2, our method achieves a notable improvement of +6.15% in accuracy and +13.60% in F1-score, demonstrating its effectiveness in image classification.

We investigate the statistical and computational limits of latent \textbf{Di}ffusion \textbf{T}ransformers (\textbf{DiT}s) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs score function, as well as the distribution recovery property of the initial data. Specifically, under mild data assumptions, we derive an approximation error bound for the score network of latent DiTs, which is sub-linear in the latent space dimension. Additionally, we derive the corresponding sample complexity bound and show that the data distribution generated from the estimated score function converges toward a proximate area of the original one. Computationally, we characterize the hardness of both forward inference and backward computation of latent DiTs, assuming the Strong Exponential Time Hypothesis (SETH). For forward inference, we identify efficient criteria for all possible latent DiTs inference algorithms and showcase our theory by pushing the efficiency toward almost-linear time inference. For backward computation, we leverage the low-rank structure within the gradient computation of DiTs training for possible algorithmic speedup. Specifically, we show that such speedup achieves almost-linear time latent DiTs training by casting the DiTs gradient as a series of chained low-rank approximations with bounded error. Under the low-dimensional assumption, we show that the convergence rate and the computational efficiency are both dominated by the dimension of the subspace, suggesting that latent DiTs have the potential to bypass the challenges associated with the high dimensionality of initial data.