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Image / Video Generation 训练优化

Deep-Unfolded Coordination

arXiv 2026-06-18

Distributed optimization is a highly scalable and structurally transparent technique to solve multi-agent robotics problems; however, such methods often suffer from the need for highly-specialized, problem-specific hyperparameter tunings. In this work, we propose Deep Coordinator, a deep-unfolding framework that learns to dynamically adjust the hyperparameters of ADMM-DDP, a popular distributed solver for robotics tasks, at solve-time in response to optimizer performance. Our architecture consists of unrolling a fixed number of ADMM-DDP iterations into a neural network with learnable functions between layers mapping the optimizer state to the next hyperparameters. To the best of our knowledge, Deep Coordinator is the first deep-unfolding framework to adapt the penalty parameters of a non-convex optimizer at solve-time; we show that the mainstream supervised approach can yield degenerate solutions when training such models, and propose an unsupervised learning scheme. On simulations with fleets of cars and quadrotors, Deep Coordinator produces trajectories of comparable quality 6.18-9.44x faster than conventional solvers. Furthermore, Deep Coordinator retains its performance benefits when deployed to systems up to 8x larger than trained on.

MedRLM: Recursive Multimodal Health Intelligence for Long-Context Clinical Reasoning, Sensor-Guided Screening, Evidence-Grounded Decision Support, and Community-to-Tertiary Referral Optimization

arXiv 2026-06-18

Real-world clinical decision support requires reasoning over heterogeneous and longitudinal patient information rather than answering isolated medical questions. However, current medical large language models and retrieval-augmented generation systems often rely on single-step prompting or retrieval, which can be fragile when clinical evidence is distributed across long electronic health records, medical images, sensor streams, guidelines, and referral constraints. This paper proposes MedRLM, a Recursive Multimodal Health Intelligence framework for long-context clinical reasoning, sensor-guided screening, and community-to-tertiary referral support. Instead of compressing all patient information into one prompt, MedRLM treats the patient case as an external clinical environment that can be recursively inspected, decomposed, retrieved, verified, and synthesized. The framework coordinates specialized agents for clinical text, longitudinal EHR, medical imaging, physiological sensor signals, guideline retrieval, uncertainty auditing, and referral planning. It further introduces a Clinical Evidence Graph Memory to connect patient-specific observations with retrieved evidence, standardized definitions, sensor-derived biomarkers, and referral criteria. A sensor-guided recursive triggering mechanism activates deeper reasoning when abnormal physiological or behavioral patterns are detected, while uncertainty-gated refinement supports clinician review for high-risk or low-confidence cases. We also outline a real-data evaluation design using public and credentialed clinical datasets spanning EHR, radiology, ECG, ICU time series, and referral-proxy outcomes. MedRLM aims to move medical AI from static question answering toward auditable, multimodal, and workflow-aware clinical decision support.

Randomized Sketching is Robust to Low-Precision Rounding on GPUs

arXiv 2026-06-18

Randomized sketching is a core primitive in randomized numerical linear algebra. On modern hardware architectures, in particular on GPUs, the performance of sparse sketches is limited by memory traffic and atomic accumulation rather than floating-point throughput. This makes sketching a natural target for mixed precision, provided that low-precision accumulation does not degrade the embedding quality. We study mixed-precision GPU implementations of sparse oblivious subspace embeddings, focusing on a SparseStack generalization of the GPU CountSketch kernel of Higgins et al. SparseStack improves embedding quality relative to CountSketch on coherent inputs, but its additional nonzeros per column increase atomic-update contention and reduce throughput. We therefore implement FP16 SparseStack variants using deterministic round-to-nearest, exact stochastic rounding, and dithered rounding, and compare them with FP32 SparseStack, CountSketch, mixed-precision CountSketch, and FlashSketch. Our main empirical finding is that, for the tested regimes, SparseStack embedding quality is insensitive to the FP16 rounding rule. Deterministic, stochastic, and dithered rounding FP16 SparseStack produce nearly identical subspace distortion and sketch-and-solve least-squares accuracy across incoherent, coherent, and adversarial test problems. The dominant accuracy factor is the sketch distribution rather than the quantization rule: SparseStack variants substantially improve distortion on coherent inputs, while all methods behave similarly on incoherent inputs. Since deterministic rounding has the lowest overhead, it provides the best performance--accuracy tradeoff among the FP16 SparseStack variants.

Addressing Detail Bottlenecks in Latent Diffusion for RGB-to-SWIR Image Translation

arXiv 2026-06-18

Latent diffusion models (LDMs) enable efficient image-to-image translation but discard fine spatial details during compression, degrading downstream perception tasks. We identify two bottlenecks: the autoencoder, which loses spatial information, and the conditioning pathway, which further degrades the source signal through naive downsampling. We propose two lightweight, backbone-agnostic fixes: a Source-Conditioned Autoencoder (SCAE) that injects high-resolution source features into the decoder via skip connections, and a Learnable Guidance Encoder (LGE) that replaces naive downsampling with a learned conditioning signal. Evaluated on RGB-to-SWIR translation for driving scenes with two denoiser backbones (U-Net and DiT), our approach improves detection mAP by up to 2x over the latent diffusion baseline, with up to 3.4x gains on small objects (COCO-small, <32^2 px^2), while achieving state-of-the-art FID. We further show that FID and detection performance are poorly correlated, motivating multi-axis evaluation. Results generalise zero-shot to the public RASMD benchmark. We will publicly release test data with annotations, all checkpoints, and training code.

Repurposing a Speech Classifier for Guided Diffusion-Based Speech Generation

arXiv 2026-06-18

Classifier guidance is a way to control diffusion generation by using a noise-conditioned classifier to steer the sampling process toward a target class. One drawback of classifier guidance is that it requires two separately trained models: a classifier and a diffusion model. We therefore study a more compact alternative in which a conventionally trained speech classifier is repurposed as the backbone for diffusion generation. Starting from a frozen noise-conditioned classifier in log-Mel space, we attach a lightweight subnetwork that reuses intermediate classifier representations and train only this subnetwork under a Denoising Score Matching objective. Our work shows that a pretrained classifier can be repurposed for conditional generation, providing an appealing bridge between discriminative modeling and conditional speech synthesis resulting in high speech quality within a single-backbone model, with reduced memory footprint and computational cost.

Pixel-Level Residual Diffusion Transformer: Scalable 3D CT Volume Generation

arXiv 2026-06-18

Generating high-resolution 3D CT volumes with fine details remains challenging due to substantial computational demands and optimization difficulties inherent to existing generative models. In this paper, we propose the Pixel-Level Residual Diffusion Transformer (PRDiT), a scalable generative framework that synthesizes high-quality 3D medical volumes directly at voxel-level. PRDiT introduces a two-stage training architecture comprising 1) a local denoiser in the form of an MLP-based blind estimator operating on overlapping 3D patches to separate low-frequency structures efficiently, and 2) a global residual diffusion transformer employing memory-efficient attention to model and refine high-frequency residuals across entire volumes. This coarse-to-fine modeling strategy simplifies optimization, enhances training stability, and effectively preserves subtle structures without the limitations of an autoencoder bottleneck. Extensive experiments conducted on the LIDC-IDRI and RAD-ChestCT datasets demonstrate that PRDiT consistently outperforms state-of-the-art models, such as HA-GAN, 3D LDM and WDM-3D, achieving significantly lower 3D FID, MMD and Wasserstein distance scores.

Pulse: Training Acceleration for Large Diffusion Models with Automatic Pipeline Parallelism

arXiv 2026-06-17

Diffusion models are now a dominant approach for high-fidelity image and video generation, yet scaling their training across GPU clusters remains challenging. Unlike transformer-only architectures, diffusion backbones commonly adopt UNet-style encoder-decoder structures with heterogeneous layers and long-range skip connections. Under conventional pipeline parallelism, these non-local dependencies force large skip activations and their gradients to traverse multiple pipeline boundaries, making peer-to-peer (P2P) communication a dominant bottleneck and substantially reducing pipeline efficiency. In this paper, we present PULSE, an automatic pipeline-parallel training strategy that makes skip locality a first-class optimization objective. PULSE eliminates skip-induced communication by collocating skip-connected encoder-decoder layers on the same device and caching skip activations locally for later use in backpropagation. To realize this placement while maintaining high pipeline utilization, PULSE co-designs: (1) a skip-aware dynamic-programming partitioner that balances heterogeneous stage workloads under symmetric collocation constraints, (2) an ILP-based schedule synthesizer that generates bubble-efficient wave schedules for the resulting stage-to-device mapping, and (3) a hybrid parallelism tuner that selects pipeline/data-parallel degrees and microbatch sizes under memory and network constraints. Our extensive experiments show that the volume of communication can be reduced by 89 percent, and the training throughput can be increased by up to 2.3x on communication-bound hardware, compared with state-of-the-art parallelism strategies.

Spotlight: Synergizing Seed Exploration and Spot GPUs for DiT RL Post-Training

arXiv 2026-06-17

Reinforcement learning (RL) post-training of Diffusion Transformers (DiTs) is prohibitively expensive, requiring thousands of high-end GPUs. Existing works explore two directions to reduce cost: seed exploration improves training convergence by selecting high-contrast samples, yet adds compute to the critical path; spot GPUs offer 69--77\% lower cost, yet sit idle during training because DiT rollouts finish nearly simultaneously, which prevents LLM-style pipelining of rollout with training. Spot preemptions further break Sequence Parallelism (SP) groups, fragmenting GPU topology. We present Spotlight, the first system that harvests spot GPUs for DiT RL post-training. Spotlight rests on two key insights we devise: (1)~we show that exploration can tolerate stale model weights because exploration that uses the model weights from the previous iteration preserves the relative ranking of random seeds, allowing exploration to run on idle spot GPUs during training. (2)~SP reconfiguration can reuse on-node state, reducing group recovery from minutes to sub-second launches. Built on these insights, Spotlight introduces three techniques: a bandit-based exploration planner that maximizes reward variance within the training time budget, elastic sequence parallelism that reconfigures SP groups on the fly via persistent schedulers and intra-node weight copying, and a preemption-aware pull-based request scheduler that balances load and commits in-flight state upon preemption. We implement Spotlight on the open-source RL platform ROLL and evaluate it on Qwen-Image post-training. Spotlight reaches the same target validation score \(4\times\) faster than baselines, reducing total cost by \(1.4\)-\(6.4\times\) while achieving superior image quality on DeepSeek-OCR and Geneval datasets with resolution \(512\times512\) and \(1280\times1280\).

PermaVid: Consistent Video Generation Across Edits via Disentangled Context Memory

arXiv 2026-06-15

Consistent video generation under editing operations requires persistence: when edits modify scene appearance or layout, subsequent generations should remain coherent across time and viewpoints. However, existing memory designs struggle to maintain long-term consistency after such modifications, as stored contexts may become outdated or invalid. To address this, we propose PermaVid, a novel framework built upon a multi-modal context memory that disentangles spatial context into semantic appearance and geometric structure, together with an edit-aware memory update and retrieval strategy that keeps memory evolution aligned with subsequent observations. Specifically, we develop two complementary memory banks: an RGB context memory that captures appearance-aware observations while implicitly encoding geometry, and a depth context memory that preserves geometry-only structure disentangled from semantics. Building on this design, we introduce a memory-guided video generation model that performs multi-modal feature fusion under reference conditions drawn from mixed-modality memory contexts. Experiments demonstrate that our method maintains strong long-term semantic and structural consistency after edits, significantly outperforming state-of-the-art methods.

Training and Evaluating Diffusion Policies with Long Context Lengths

arXiv 2026-06-15

Imitation learning has enabled highly-dexterous robotic manipulation from RGB observations. Policies trained with these methods, however, typically condition robot actions on only a short history of observations. These policies cannot solve tasks that require memory and can get stuck repeatedly executing the same failing motions. In this work, we first benchmark policy performance as context length is incrementally increased from short to long, across a spectrum of tasks with varying local stability and memory requirements, and in multiple data regimes. To our knowledge, this is the first study to investigate context length in imitation learning at this level of detail. Our results challenge prior claims: naively scaling context length is not as brittle as advertised in literature. With an appropriate conditioning method and denoising backbone (UNet+Cross-Attention), single-task policies achieve high success rates on many tasks in the usual data regime even with naive scaling. Next, we propose a training algorithm to jointly train policies at multiple context lengths, further reducing the sample complexity of long-context learning. Finally, we apply our findings to re-evaluate some previously proposed solutions to long-context imitation learning.

Diffusion Offline Reinforcement Learning for Fair and Energy-Efficient UAV-Assisted Wireless Networks

arXiv 2026-06-15

The integration of generative artificial intelligence with wireless communication and signal processing systems has opened new avenues for intelligent, data-driven decision-making in future 6G networks. This work proposes a diffusion soft actor-critic (Diffusion-SAC) approach that leverages offline reinforcement learning (RL) enhanced by denoising diffusion probabilistic models (DDPMs) to optimize trajectory and scheduling control in unmanned aerial vehicle (UAV) networks. While offline RL methods, such as conservative Q-learning (CQL), can learn from static datasets, they often struggle to generalize in low-data or dynamic conditions. To address this, we combine the robustness of CQL with the generative power of diffusion models, enabling expressive and signal-aware policy learning that generalizes beyond behavior policies. Applied to a UAV-assisted wireless network, the proposed framework minimizes transmission energy and improves fairness among devices. Simulations show that Diffusion-SAC outperforms standard offline RL baselines, achieving more stable convergence and higher rewards even with limited datasets. The method enhances data efficiency, reduces energy consumption, and increases throughput by more than 35 % compared to existing algorithms, demonstrating its potential for robust policy learning in next-generation wireless control systems.

ARGUS: Stacked Multi-View Identity Mosaic Injection for Subject-Preserving Video Generation

arXiv 2026-06-10

Subject-preserving video generation is not solved by frontal-face similarity alone: a generated person must remain recognizable across motion, large viewpoint changes, expression shifts, occlusion, scale variation, and conflicts among text, first-frame, and identity references. We argue that the central bottleneck is the point-reference paradigm, which collapses identity into a single static observation entangled with pose, accessories, lighting, background, and camera statistics. We introduce Argus, a Wan-based framework centered on Stacked Multi-View Identity Mosaic Injection (SMII). SMII converts MLLM-selected image/video identity evidence into a 3*3 stacked mosaic, synchronizes the mosaic with the current diffusion time, and injects it as negative-time read-only memory in Wan's native token space. This turns identity from an external clean adapter or a single reference image into a compact dynamic distribution. Around SMII, an MLLM Identity Director selects informative identity moments and resolves condition conflicts, while no-cross-pair counterfactual training, Temporal Identity Annealing, and Adaptive Self-Likeness Guidance improve robustness without paired subject-video supervision. We further release HardID-Celeb, a public-figure identity-stress benchmark, and introduce YawScore and OccScore to probe large-yaw and first-frame-occlusion robustness. Argus achieves state-of-the-art results on OpenS2V-Eval Human-Domain, reaching 64.38 Total Score, 71.86 FaceSim, 51.62 NexusScore, and 79.14 NaturalScore. On HardID-Celeb, Argus obtains 76.80 FaceSim and improves YawScore and OccScore by 12.60 and 15.10 points over the strongest baselines, demonstrating that dynamic identity memory and large-scale counterfactual self-supervision are highly effective for subject-preserving video generation.

FadeMem: Distance-Aware Memory Consolidation for Autoregressive Video Diffusion

arXiv 2026-06-09

Autoregressive video generators synthesize long videos by generating successive temporal segments, but their historical KV cache grows with video length. Existing bounded-cache methods reduce this cost with local windows, sink tokens, or compressed memory states, yet they usually assign fixed roles to different parts of the history. We propose FadeMem, a distance-aware KV memory consolidation mechanism that organizes historical KV blocks into a temporal hierarchy under a fixed cache budget. This design is motivated by frequency-dependent temporal decay: fine details decorrelate quickly, while coarse scene structure and identity remain useful over longer horizons. During generation, new history is inserted as fine-grained entries, while older adjacent entries are progressively merged under a power-law temporal allocation schedule, yielding a dense-near, sparse-far memory within one cache. Without architectural changes, FadeMem preserves recent context for short-term dynamics and compact long-range anchors for identity and scene coherence. Experiments show improved subject consistency, background stability, and temporal coherence over existing bounded-cache strategies.

Unified Energy for Invariant and Independent Decoding in Diffusion Language Models

arXiv 2026-06-08

Diffusion Language Models (DLMs) enable parallel text generation by iteratively denoising a full sequence, offering attractive flexibility compared to auto-regressive (AR) decoding. However, existing methods fail to fully capture token relationships, leading to a performance gap relative to AR baselines, especially as the degree of parallelism increases. In this paper, we give a systematic analysis of the gap, identifying three key factors: (i) model capacity, (ii) dependency, and (iii) invariance. To address these issues, we first propose an invariant energy (Inv-E) together with an effective sampling-based estimator to handle the invariance issue. By further combining with the independent energy (Ind-E), we obtain a unified energy (Uni-E), that accounts for all these factors. Uni-E enjoys a unique advantage: it can be computed exactly without sampling-based partition estimation. Besides, Uni-E is model agnostic and can therefore be scaled to models of arbitrary size. We further prove that Uni-E can correct the distribution shift caused by dependency and invariance. Extensive experiments across Diffusion Language Models (DLMs) and Diffusion Large Language Models (DLLMs) demonstrate the effectiveness of the proposed Uni-E.

Rethinking 3D Shape Generation: Diffusion over Superquadrics

arXiv 2026-06-08

Diffusion models have advanced 3D shape generation, yet most methods still denoise in high-cardinality spaces (e.g., voxel/SDF grids, meshes, or point clouds), which is computationally and memory intensive and makes it difficult to scale in terms of both higher resolution and stronger controllability. We rethink the diffusion representation and propose to move diffusion from dense geometry to compact geometric primitives, representing each shape as a small set of superquadrics. Instead of operating on thousands to millions of geometric representation values, we leverage 7KB superquadric parameters (pose, size, and shape), drastically reducing diffusion-state dimensionality and per-step compute/memory. Our diffusion-over-superquadrics improves scalability by supporting broader capabilities (e.g., resolution-free point-cloud decoding, part-level editing, and constraint-based design) and achieving competitive surface-fidelity and distributional performance on standard benchmarks after point-cloud decoding, while enabling efficient generation within 0.6s per shape for most conditions.

STaR-Quant: State-Time Consistent Post-Training Quantization for Diffusion Large Language Models

arXiv 2026-06-03

Diffusion large language models (DLLMs) have recently emerged as a promising alternative to autoregressive LLMs by generating text through iterative masked denoising with bidirectional context. However, their large model sizes and iterative denoising process introduce substantial memory and computational overhead, motivating post-training quantization for efficient deployment. In this paper, we identify two key challenges for low-bit DLLM quantization: state-dependent activation disparity and temporal error accumulation. Masked and unmasked tokens exhibit different activation distributions within each denoising step, while quantization errors can accumulate across steps during iterative decoding. To address these challenges, we propose STaR-Quant, a state-time consistent PTQ framework for DLLMs. STaR-Quant introduces State-Guided Activation Transformation (SGAT) to assign masked and unmasked tokens to different activation transformation spaces with a unified static weight-side transformation. It further introduces Temporal Attention Compensation (TAC) to correct the quantized attention representation via a lightweight block-diagonal affine mapping. Experiments on representative DLLMs demonstrate that STaR-Quant consistently improves low-bit weight-activation quantization over strong PTQ baselines, while delivering up to 1.69x speedup and 3.14x memory saving over FP16 deployment.

LongLive-RAG: A General Retrieval-Augmented Framework for Long Video Generation

arXiv 2026-06-01

Autoregressive (AR) video diffusion enables variable-length synthesis, but long-horizon generation often suffers from accumulated errors and identity drift. For efficiency, existing methods commonly adopt sliding-window attention during generation. This creates an irreversible generation trajectory: once the active window accumulates appearance errors, subsequent generations can only condition on this degraded trajectory and drift further away. We address this limitation by formulating long video generation as a retrieval-augmented generation (RAG) problem. Rather than relying solely on the recent window, we treat previously generated latents as a dynamic, searchable history. We propose LongLive-RAG, a general retrieval framework for AR video generation. At each new block, LongLive-RAG uses a query embedding to retrieve relevant historical latents. This lightweight retrieval step adds only a small overhead relative to generation and lets the generator condition on non-local context instead of only the recent window. To make retrieval more discriminative, we introduce the Window Temporal Delta Loss that suppresses redundant local similarity and encourages embeddings to capture meaningful temporal changes. Together, these components help reduce error accumulation caused by sliding-window attention. Experiments across multiple AR backbones and generation lengths show improved long-video quality and the best average VBench-Long rank. To our knowledge, among open-ended AR long video generation methods, LongLive-RAG is the first to formulate self-generated latent history as content-addressable retrieval memory. Code is available at https://github.com/qixinhu11/LongLive-RAG.

SafeGen-Bench: Benchmarking Safety in Image-Conditioned Text-to-Video Generation

arXiv 2026-05-31

With the rapid advancements in text-to-image diffusion models, generative video models (T2V models) like Sora can now produce short synthetic videos from a text prompt or an initial image. However, synthetic video generation -- especially when guided by an initial image -- often poses risks, including the potential creation of illegal, politically sensitive, or unethical content. Existing benchmarks have started to consider the safety of generated videos, but they primarily focus on testing models with malicious text prompts, ignoring the scenario where text prompt and image combination may still lead to harmful video content. In practice, this is a common and challenging issue: videos generated from safe text and image inputs can nonetheless convey harmful information. To bridge this gap, we introduce SafeGen-Bench, a benchmark specifically designed to evaluate the safety of conditional T2V models. Our benchmark defines 10 malicious categories, concentrating on risks related to both temporal sequences and depicted behaviors. SafeGen-Bench consists of carefully selected start frames from diverse image and video sources, paired with corresponding text prompts to simulate realistic inputs. We evaluate a variety of conditional T2V models on SafeGen-Bench, and the results indicate that current models struggle to consistently avoid generating malicious content with unsafety scores reaching up to 44.5, especially under conditions requiring high quality. Furthermore, we assess the effectiveness of both text-based and image-based guardrails on our benchmark, finding that unimodal guardrails alone were insufficient to provide a robust defense, with an 80\% failure rate across seven malicious categories. We hope that SafeGen-Bench will foster the development of safer and more controllable conditional T2V models.

Decoupled Residual Denoising Diffusion Models for Unified and Data Efficient Image-to-Image Translation

arXiv 2026-05-31

We propose Decoupled Residual Denoising Diffusion models (DRDD) for unified and data-efficient image-to-image (I2I) translation. While diffusion models have advanced I2I translation in terms of quality and diversity, we uncover a previously under-explored property in diffusion models. Crucially, beyond its conventional role of manifold lifting (i.e., moving data off low-dimensional manifolds), injecting Gaussian noise facilitates domain harmonization by implicitly aligning feature distributions across domains, a property particularly advantageous for unified I2I translation. However, existing diffusion models prematurely erode this harmonization effect, as noise and residuals are simultaneously removed in a single coupled diffusion process. To address this, DRDD decouples the diffusion process into two sequential and independent diffusion stages: (1) a stochastic noise diffusion for domain harmonization and manifold lifting, and (2) a deterministic residual diffusion that learns the core semantic mapping entirely within the fixed-noise domain. This decoupling preserves harmonization and manifold lifting effects throughout the transformation, substantially simplifying the learning of unified mappings across diverse tasks and domains. Notably, the noise diffusion stage is trained exclusively on abundant, unpaired target-domain images, greatly improving data efficiency. Comprehensive theoretical and empirical analysis demonstrates that DRDD is broadly compatible with mainstream diffusion models and consistently delivers robust, unified I2I translation, even under limited paired data. Our code is available at https://github.com/HKU-HealthAI/DRDD.

Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions

arXiv 2026-05-28

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their statistical efficiency remains limited. Existing theories typically rely on strong regularity assumptions, such as uniformly bounded densities or globally smooth score functions, which fail to capture such intrinsic structures. In this work, we study the sample complexity of diffusion models for learning distributions supported on a union of low-dimensional subspaces. Assuming that the data distribution within each subspace is subgaussian, we show that diffusion models require at most \(\widetilde{O}(\varepsilon^{-k \vee 2})\) samples to achieve \(\varepsilon\) error in 1-Wasserstein distance, where \(k\) is the intrinsic dimension. This near-optimal convergence rate depends only on the intrinsic dimension and significantly improves upon prior theoretical guarantees that suffer from the curse of dimensionality. Notably, our analysis applies to a broad collection of distributions without imposing smoothness, bounded-density, or log-concavity assumptions. Overall, our results show that diffusion models can statistically adapt to intrinsic low-dimensional structure while naturally accommodating multi-modal data, offering a rigorous theoretical justification for their success in complex high-dimensional learning tasks.