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An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization
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Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.
Forward citations
Cited by 19 Pith papers
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Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
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From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models
An end-to-end TV bound for score-based diffusion models that decomposes generative error into forward truncation, reverse discretization, finite-sample generalization, and optimization gap.
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From Similarity to Feasibility: Diffusion-Refined Retrieval-Augmented Generation for Distribution Network Optimization
A retrieval-and-diffusion warm-start pipeline cuts solve times for distribution-network optimization on most tested benchmarks while keeping solution quality near-optimal, but it is slower than direct solving on one c...
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Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approach
By adding drift g(t)^2 ∇log h(t,y) with h estimated via martingale and covariation losses, diffusion samples can be hard-conditioned on an event.
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Likelihood Matching for Diffusion Models
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Optimization-Free Diffusion Model -- A Perturbation Theory Approach
Score estimation in diffusion models is reformulated as solving linear systems in an eigenbasis of a backward Kolmogorov operator, avoiding neural network training and forward SDE simulation.
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Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Acceleration
A second-order local linearization sampler is shown to reach O~(1/ε) Wasserstein-2 accuracy for strongly log-concave score-based diffusion models, improving on the O~(1/ε²) rate of Euler and exponential integrator schemes.
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On Statistical Rates of Conditional Diffusion Transformers: Approximation, Estimation and Minimax Optimality
Conditional diffusion transformers and their latent variants receive score approximation and estimation rates, but the minimax optimality headline rests on setting a derived constant equal to 1/2.
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Diffusion-Based Data-Driven Assortment Optimization
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Non-Identical Diffusion Models in MIMO-OFDM Channel Generation
A diffusion model with an element-wise time matrix, rather than one global time, improves MIMO-OFDM channel recovery from unevenly reliable pilots, but the proof of correctness has gaps.
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Fast Direct: Query-Efficient Online Black-box Guidance for Diffusion-model Target Generation
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Machine-Learning-Assisted Photonic Device Development: A Multiscale Approach from Theory to Characterization
This review organizes machine-learning-assisted photonic device development into a five-step Bayesian framework spanning theory, simulation, design, fabrication, and characterization.
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Efficient Diffusion Models: A Survey
The paper organizes research on efficient diffusion models into a taxonomy spanning algorithms, systems, and frameworks, and provides a curated reference list.
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Weak Supervision Dynamic KL-Weighted Diffusion Models Guided by Large Language Models
A vague proposal for LLM-guided diffusion with dynamic KL weighting, backed by unsupported FID/IS tables.
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A data-poisoning backdoor attack on audio transformers is claimed with 100 percent success on TIMIT, but the paper provides no reproducible derivation or evaluation.
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