Anbu Huang

Anbu Huang

Research Scientist, Author, AI Enthusiast, THU

Posts by Tags

AIGC

• Unifying Discrete and Continuous Perspectives in Diffusion Models

19 minute read

Published:

Diffusion models have been shown to be a highly promising approach in the field of image generation. They treat image generation as two independent processes: the forward process, which transforms a complex data distribution into a known prior distribution (typically a standard normal distribution) by gradually injecting noise; and the reverse process, which transforms the prior distribution back into the complex data distribution by gradually removing the noise.

Acceleration

• Fast Generation with Flow Matching

23 minute read

Published:

Fast sampling has become a central goal in generative modeling, enabling the transition from high-fidelity but computationally intensive diffusion models to real-time generation systems. While diffusion models rely on tailored numerical solvers to mitigate the stiffness of their probability flow ODEs, flow matching defines dynamics through smooth interpolation paths, fundamentally altering the challenges of acceleration. This article provides a comprehensive overview of fast sampling in flow matching, with emphasis on path linearization strategies (e.g., Rectified Flow, ReFlow, SlimFlow, InstaFlow), the integration of consistency models, and emerging approaches such as flow generators.

Conditional Flow Matching

• From Diffusion to Flow: A New Genrative Paradigm

33 minute read

Published:

In this post, we uncovered the foundations of Flow Matching: the limitations of diffusion models, the constraints of continuous flows, and the transformative idea of directly learning the path between distributions. From the intuition of Rectified Flow to the unifying lens of Stochastic Interpolants, Flow Matching emerged as more than a method — it is a paradigm that reframes generation as learning currents of transformation. With this conceptual map in hand, we are now ready to move from theory to practice.

Consistency Model

• The Consistency Family: From Discrete-Time Constraints to Continuous-Time Flows

18 minute read

Published:

Consistency models (CMs) have recently emerged as a powerful paradigm for accelerating diffusion sampling by directly learning mappings that preserve consistency across noisy representations of the same data. This paper provides a comprehensive study of the Consistency Family, tracing its evolution from discrete consistency models to continuous-time formulations and trajectory-based extensions. We begin by revisiting the foundational motivation behind CMs and systematically derive their discrete and continuous objectives under both consistency distillation and consistency training paradigms.

Consistency Models

• Inverse Problems with Generative Priors

49 minute read

Published:

📚 Table of Contents

• Flow Map Learning: A Unified Framework for Fast Generation

7 minute read

Published:

A “flow map” 1 2 3 typically denotes a neural network (or parametric model)

  1. Sabour A, Fidler S, Kreis K. Align Your Flow: Scaling Continuous-Time Flow Map Distillation[J]. arXiv preprint arXiv:2506.14603, 2025. ↩

  2. Boffi N M, Albergo M S, Vanden-Eijnden E. Flow map matching with stochastic interpolants: A mathematical framework for consistency models[J]. Transactions on Machine Learning Research, 2025. ↩

  3. Hu Z, Lai C H, Mitsufuji Y, et al. CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models[J]. arXiv preprint arXiv:2509.24526, 2025. ↩

• Fast Generation with Flow Matching

23 minute read

Published:

Fast sampling has become a central goal in generative modeling, enabling the transition from high-fidelity but computationally intensive diffusion models to real-time generation systems. While diffusion models rely on tailored numerical solvers to mitigate the stiffness of their probability flow ODEs, flow matching defines dynamics through smooth interpolation paths, fundamentally altering the challenges of acceleration. This article provides a comprehensive overview of fast sampling in flow matching, with emphasis on path linearization strategies (e.g., Rectified Flow, ReFlow, SlimFlow, InstaFlow), the integration of consistency models, and emerging approaches such as flow generators.

DDIM

• Unifying Discrete and Continuous Perspectives in Diffusion Models

19 minute read

Published:

Diffusion models have been shown to be a highly promising approach in the field of image generation. They treat image generation as two independent processes: the forward process, which transforms a complex data distribution into a known prior distribution (typically a standard normal distribution) by gradually injecting noise; and the reverse process, which transforms the prior distribution back into the complex data distribution by gradually removing the noise.

DDPM

• Unifying Discrete and Continuous Perspectives in Diffusion Models

19 minute read

Published:

Diffusion models have been shown to be a highly promising approach in the field of image generation. They treat image generation as two independent processes: the forward process, which transforms a complex data distribution into a known prior distribution (typically a standard normal distribution) by gradually injecting noise; and the reverse process, which transforms the prior distribution back into the complex data distribution by gradually removing the noise.

DiT

• Diffusion Architectures Part II: Efficiency-Oriented Designs

57 minute read

Published:

Efficiency is a defining challenge for diffusion models, which often suffer from high computational cost and slow inference. This article surveys architectural strategies that enhance efficiency, from latent-space diffusion and multi-resolution cascades to lightweight convolutional blocks, efficient attention mechanisms, and parameter-efficient modules like LoRA. We also examine distillation and inference-time acceleration techniques that drastically reduce sampling steps. Together, these approaches demonstrate how architectural design can expand the reach of diffusion models — from research labs to real-time and mobile applications.

• Diffusion Architectures Part I: Stability-Oriented Designs

74 minute read

Published:

This article explores how network architectures shape the stability of diffusion model training. We contrast U-Net and Transformer-based (DiT) backbones, analyzing how skip connections, residual scaling, and normalization influence gradient propagation across noise levels. By surveying stability-oriented innovations such as AdaGN, AdaLN-Zero, and skip pathway regulation, we reveal why architectural choices can determine whether training converges smoothly or collapses. The discussion provides both theoretical insights and practical design rules for building robust diffusion models.

Diffusion Model

• Inverse Problems with Generative Priors

49 minute read

Published:

📚 Table of Contents

• Flow Map Learning: A Unified Framework for Fast Generation

7 minute read

Published:

A “flow map” 1 2 3 typically denotes a neural network (or parametric model)

  1. Sabour A, Fidler S, Kreis K. Align Your Flow: Scaling Continuous-Time Flow Map Distillation[J]. arXiv preprint arXiv:2506.14603, 2025. ↩

  2. Boffi N M, Albergo M S, Vanden-Eijnden E. Flow map matching with stochastic interpolants: A mathematical framework for consistency models[J]. Transactions on Machine Learning Research, 2025. ↩

  3. Hu Z, Lai C H, Mitsufuji Y, et al. CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models[J]. arXiv preprint arXiv:2509.24526, 2025. ↩

• High-Order PF-ODE Solver in Diffusion Models

40 minute read

Published:

Diffusion sampling can be cast as integrating the probability flow ODE (PF-ODE), but dropping it into a generic ODE toolbox rarely delivers the best speed–quality trade-off. This post first revisits core numerical-analysis ideas. It then explains why vanilla integrators underperform on the semi-linear, sometimes stiff PF-ODE in low-NFE regimes, and surveys families that exploit diffusion-specific structure: pseudo-numerical samplers (PLMS/PNDM) and semi-analytic/high-order solvers (DEIS, DPM-Solver/++/UniPC). The goal is a practical, unified view of when and why these PF-ODE samplers work beyond “just use RK4.”

• Accelerating Diffusion Sampling: From Multi-Step to Single-step Generation

66 minute read

Published:

This article takes a deep dive into the evolution of diffusion model sampling techniques, tracing the progression from early score-based models with Langevin Dynamics, through discrete and non-Markov diffusion processes, to continuous-time SDE/ODE formulations, specialized numerical solvers, and cutting-edge methods such as consistency models, distillation, and flow matching. Our goal is to provide both a historical perspective and a unified theoretical framework to help readers understand not only how these methods work but why they were developed.

• The Consistency Family: From Discrete-Time Constraints to Continuous-Time Flows

18 minute read

Published:

Consistency models (CMs) have recently emerged as a powerful paradigm for accelerating diffusion sampling by directly learning mappings that preserve consistency across noisy representations of the same data. This paper provides a comprehensive study of the Consistency Family, tracing its evolution from discrete consistency models to continuous-time formulations and trajectory-based extensions. We begin by revisiting the foundational motivation behind CMs and systematically derive their discrete and continuous objectives under both consistency distillation and consistency training paradigms.

• Diffusion Architectures Part II: Efficiency-Oriented Designs

57 minute read

Published:

Efficiency is a defining challenge for diffusion models, which often suffer from high computational cost and slow inference. This article surveys architectural strategies that enhance efficiency, from latent-space diffusion and multi-resolution cascades to lightweight convolutional blocks, efficient attention mechanisms, and parameter-efficient modules like LoRA. We also examine distillation and inference-time acceleration techniques that drastically reduce sampling steps. Together, these approaches demonstrate how architectural design can expand the reach of diffusion models — from research labs to real-time and mobile applications.

• Diffusion Architectures Part I: Stability-Oriented Designs

74 minute read

Published:

This article explores how network architectures shape the stability of diffusion model training. We contrast U-Net and Transformer-based (DiT) backbones, analyzing how skip connections, residual scaling, and normalization influence gradient propagation across noise levels. By surveying stability-oriented innovations such as AdaGN, AdaLN-Zero, and skip pathway regulation, we reveal why architectural choices can determine whether training converges smoothly or collapses. The discussion provides both theoretical insights and practical design rules for building robust diffusion models.

• Unifying Discrete and Continuous Perspectives in Diffusion Models

19 minute read

Published:

Diffusion models have been shown to be a highly promising approach in the field of image generation. They treat image generation as two independent processes: the forward process, which transforms a complex data distribution into a known prior distribution (typically a standard normal distribution) by gradually injecting noise; and the reverse process, which transforms the prior distribution back into the complex data distribution by gradually removing the noise.

Diffusion Model Training

• Analysis of the Stability and Efficiency of Diffusion Model Training

73 minute read

Published:

while diffusion models have revolutionized generative AI, their training challenges stem from a combination of resource intensity, optimization intricacies, and deployment hurdles. A stable training process ensures that the model produces good quality samples and converges efficiently over time without suffering from numerical instabilities.

Discussion Models

• From Diffusion to Flow: A New Genrative Paradigm

33 minute read

Published:

In this post, we uncovered the foundations of Flow Matching: the limitations of diffusion models, the constraints of continuous flows, and the transformative idea of directly learning the path between distributions. From the intuition of Rectified Flow to the unifying lens of Stochastic Interpolants, Flow Matching emerged as more than a method — it is a paradigm that reframes generation as learning currents of transformation. With this conceptual map in hand, we are now ready to move from theory to practice.

Distillation

• Inverse Problems with Generative Priors

49 minute read

Published:

📚 Table of Contents

• Flow Map Learning: A Unified Framework for Fast Generation

7 minute read

Published:

A “flow map” 1 2 3 typically denotes a neural network (or parametric model)

  1. Sabour A, Fidler S, Kreis K. Align Your Flow: Scaling Continuous-Time Flow Map Distillation[J]. arXiv preprint arXiv:2506.14603, 2025. ↩

  2. Boffi N M, Albergo M S, Vanden-Eijnden E. Flow map matching with stochastic interpolants: A mathematical framework for consistency models[J]. Transactions on Machine Learning Research, 2025. ↩

  3. Hu Z, Lai C H, Mitsufuji Y, et al. CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models[J]. arXiv preprint arXiv:2509.24526, 2025. ↩

EDM

• Analysis of the Stability and Efficiency of Diffusion Model Training

73 minute read

Published:

while diffusion models have revolutionized generative AI, their training challenges stem from a combination of resource intensity, optimization intricacies, and deployment hurdles. A stable training process ensures that the model produces good quality samples and converges efficiently over time without suffering from numerical instabilities.

ELBO

• Analysis of the Stability and Efficiency of Diffusion Model Training

73 minute read

Published:

while diffusion models have revolutionized generative AI, their training challenges stem from a combination of resource intensity, optimization intricacies, and deployment hurdles. A stable training process ensures that the model produces good quality samples and converges efficiently over time without suffering from numerical instabilities.

EMA

• Analysis of the Stability and Efficiency of Diffusion Model Training

73 minute read

Published:

while diffusion models have revolutionized generative AI, their training challenges stem from a combination of resource intensity, optimization intricacies, and deployment hurdles. A stable training process ensures that the model produces good quality samples and converges efficiently over time without suffering from numerical instabilities.

Efficiency

• Analysis of the Stability and Efficiency of Diffusion Model Training

73 minute read

Published:

while diffusion models have revolutionized generative AI, their training challenges stem from a combination of resource intensity, optimization intricacies, and deployment hurdles. A stable training process ensures that the model produces good quality samples and converges efficiently over time without suffering from numerical instabilities.

Flow

• The Consistency Family: From Discrete-Time Constraints to Continuous-Time Flows

18 minute read

Published:

Consistency models (CMs) have recently emerged as a powerful paradigm for accelerating diffusion sampling by directly learning mappings that preserve consistency across noisy representations of the same data. This paper provides a comprehensive study of the Consistency Family, tracing its evolution from discrete consistency models to continuous-time formulations and trajectory-based extensions. We begin by revisiting the foundational motivation behind CMs and systematically derive their discrete and continuous objectives under both consistency distillation and consistency training paradigms.

Flow Matching

• Inverse Problems with Generative Priors

49 minute read

Published:

📚 Table of Contents

• Flow Map Learning: A Unified Framework for Fast Generation

7 minute read

Published:

A “flow map” 1 2 3 typically denotes a neural network (or parametric model)

  1. Sabour A, Fidler S, Kreis K. Align Your Flow: Scaling Continuous-Time Flow Map Distillation[J]. arXiv preprint arXiv:2506.14603, 2025. ↩

  2. Boffi N M, Albergo M S, Vanden-Eijnden E. Flow map matching with stochastic interpolants: A mathematical framework for consistency models[J]. Transactions on Machine Learning Research, 2025. ↩

  3. Hu Z, Lai C H, Mitsufuji Y, et al. CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models[J]. arXiv preprint arXiv:2509.24526, 2025. ↩

• Fast Generation with Flow Matching

23 minute read

Published:

Fast sampling has become a central goal in generative modeling, enabling the transition from high-fidelity but computationally intensive diffusion models to real-time generation systems. While diffusion models rely on tailored numerical solvers to mitigate the stiffness of their probability flow ODEs, flow matching defines dynamics through smooth interpolation paths, fundamentally altering the challenges of acceleration. This article provides a comprehensive overview of fast sampling in flow matching, with emphasis on path linearization strategies (e.g., Rectified Flow, ReFlow, SlimFlow, InstaFlow), the integration of consistency models, and emerging approaches such as flow generators.

• From Diffusion to Flow: A New Genrative Paradigm

33 minute read

Published:

In this post, we uncovered the foundations of Flow Matching: the limitations of diffusion models, the constraints of continuous flows, and the transformative idea of directly learning the path between distributions. From the intuition of Rectified Flow to the unifying lens of Stochastic Interpolants, Flow Matching emerged as more than a method — it is a paradigm that reframes generation as learning currents of transformation. With this conceptual map in hand, we are now ready to move from theory to practice.

Generative Models

• From Diffusion to Flow: A New Genrative Paradigm

33 minute read

Published:

In this post, we uncovered the foundations of Flow Matching: the limitations of diffusion models, the constraints of continuous flows, and the transformative idea of directly learning the path between distributions. From the intuition of Rectified Flow to the unifying lens of Stochastic Interpolants, Flow Matching emerged as more than a method — it is a paradigm that reframes generation as learning currents of transformation. With this conceptual map in hand, we are now ready to move from theory to practice.

Gradient Clipping

• Analysis of the Stability and Efficiency of Diffusion Model Training

73 minute read

Published:

while diffusion models have revolutionized generative AI, their training challenges stem from a combination of resource intensity, optimization intricacies, and deployment hurdles. A stable training process ensures that the model produces good quality samples and converges efficiently over time without suffering from numerical instabilities.

Langevin Dynamics

• Accelerating Diffusion Sampling: From Multi-Step to Single-step Generation

66 minute read

Published:

This article takes a deep dive into the evolution of diffusion model sampling techniques, tracing the progression from early score-based models with Langevin Dynamics, through discrete and non-Markov diffusion processes, to continuous-time SDE/ODE formulations, specialized numerical solvers, and cutting-edge methods such as consistency models, distillation, and flow matching. Our goal is to provide both a historical perspective and a unified theoretical framework to help readers understand not only how these methods work but why they were developed.

Loss weighting

• Analysis of the Stability and Efficiency of Diffusion Model Training

73 minute read

Published:

while diffusion models have revolutionized generative AI, their training challenges stem from a combination of resource intensity, optimization intricacies, and deployment hurdles. A stable training process ensures that the model produces good quality samples and converges efficiently over time without suffering from numerical instabilities.

Mixed Precision Training

• Analysis of the Stability and Efficiency of Diffusion Model Training

73 minute read

Published:

while diffusion models have revolutionized generative AI, their training challenges stem from a combination of resource intensity, optimization intricacies, and deployment hurdles. A stable training process ensures that the model produces good quality samples and converges efficiently over time without suffering from numerical instabilities.

NCSN

• Unifying Discrete and Continuous Perspectives in Diffusion Models

19 minute read

Published:

Diffusion models have been shown to be a highly promising approach in the field of image generation. They treat image generation as two independent processes: the forward process, which transforms a complex data distribution into a known prior distribution (typically a standard normal distribution) by gradually injecting noise; and the reverse process, which transforms the prior distribution back into the complex data distribution by gradually removing the noise.

Normalizing Flows

• From Diffusion to Flow: A New Genrative Paradigm

33 minute read

Published:

In this post, we uncovered the foundations of Flow Matching: the limitations of diffusion models, the constraints of continuous flows, and the transformative idea of directly learning the path between distributions. From the intuition of Rectified Flow to the unifying lens of Stochastic Interpolants, Flow Matching emerged as more than a method — it is a paradigm that reframes generation as learning currents of transformation. With this conceptual map in hand, we are now ready to move from theory to practice.

Numerical Computation

• High-Order PF-ODE Solver in Diffusion Models

40 minute read

Published:

Diffusion sampling can be cast as integrating the probability flow ODE (PF-ODE), but dropping it into a generic ODE toolbox rarely delivers the best speed–quality trade-off. This post first revisits core numerical-analysis ideas. It then explains why vanilla integrators underperform on the semi-linear, sometimes stiff PF-ODE in low-NFE regimes, and surveys families that exploit diffusion-specific structure: pseudo-numerical samplers (PLMS/PNDM) and semi-analytic/high-order solvers (DEIS, DPM-Solver/++/UniPC). The goal is a practical, unified view of when and why these PF-ODE samplers work beyond “just use RK4.”

• Accelerating Diffusion Sampling: From Multi-Step to Single-step Generation

66 minute read

Published:

This article takes a deep dive into the evolution of diffusion model sampling techniques, tracing the progression from early score-based models with Langevin Dynamics, through discrete and non-Markov diffusion processes, to continuous-time SDE/ODE formulations, specialized numerical solvers, and cutting-edge methods such as consistency models, distillation, and flow matching. Our goal is to provide both a historical perspective and a unified theoretical framework to help readers understand not only how these methods work but why they were developed.

ODE

• High-Order PF-ODE Solver in Diffusion Models

40 minute read

Published:

Diffusion sampling can be cast as integrating the probability flow ODE (PF-ODE), but dropping it into a generic ODE toolbox rarely delivers the best speed–quality trade-off. This post first revisits core numerical-analysis ideas. It then explains why vanilla integrators underperform on the semi-linear, sometimes stiff PF-ODE in low-NFE regimes, and surveys families that exploit diffusion-specific structure: pseudo-numerical samplers (PLMS/PNDM) and semi-analytic/high-order solvers (DEIS, DPM-Solver/++/UniPC). The goal is a practical, unified view of when and why these PF-ODE samplers work beyond “just use RK4.”

• Accelerating Diffusion Sampling: From Multi-Step to Single-step Generation

66 minute read

Published:

This article takes a deep dive into the evolution of diffusion model sampling techniques, tracing the progression from early score-based models with Langevin Dynamics, through discrete and non-Markov diffusion processes, to continuous-time SDE/ODE formulations, specialized numerical solvers, and cutting-edge methods such as consistency models, distillation, and flow matching. Our goal is to provide both a historical perspective and a unified theoretical framework to help readers understand not only how these methods work but why they were developed.

• Unifying Discrete and Continuous Perspectives in Diffusion Models

19 minute read

Published:

Diffusion models have been shown to be a highly promising approach in the field of image generation. They treat image generation as two independent processes: the forward process, which transforms a complex data distribution into a known prior distribution (typically a standard normal distribution) by gradually injecting noise; and the reverse process, which transforms the prior distribution back into the complex data distribution by gradually removing the noise.

Rectified Flow

• From Diffusion to Flow: A New Genrative Paradigm

33 minute read

Published:

In this post, we uncovered the foundations of Flow Matching: the limitations of diffusion models, the constraints of continuous flows, and the transformative idea of directly learning the path between distributions. From the intuition of Rectified Flow to the unifying lens of Stochastic Interpolants, Flow Matching emerged as more than a method — it is a paradigm that reframes generation as learning currents of transformation. With this conceptual map in hand, we are now ready to move from theory to practice.

SDE

• Unifying Discrete and Continuous Perspectives in Diffusion Models

19 minute read

Published:

Diffusion models have been shown to be a highly promising approach in the field of image generation. They treat image generation as two independent processes: the forward process, which transforms a complex data distribution into a known prior distribution (typically a standard normal distribution) by gradually injecting noise; and the reverse process, which transforms the prior distribution back into the complex data distribution by gradually removing the noise.

Sampling

• High-Order PF-ODE Solver in Diffusion Models

40 minute read

Published:

Diffusion sampling can be cast as integrating the probability flow ODE (PF-ODE), but dropping it into a generic ODE toolbox rarely delivers the best speed–quality trade-off. This post first revisits core numerical-analysis ideas. It then explains why vanilla integrators underperform on the semi-linear, sometimes stiff PF-ODE in low-NFE regimes, and surveys families that exploit diffusion-specific structure: pseudo-numerical samplers (PLMS/PNDM) and semi-analytic/high-order solvers (DEIS, DPM-Solver/++/UniPC). The goal is a practical, unified view of when and why these PF-ODE samplers work beyond “just use RK4.”

• Accelerating Diffusion Sampling: From Multi-Step to Single-step Generation

66 minute read

Published:

This article takes a deep dive into the evolution of diffusion model sampling techniques, tracing the progression from early score-based models with Langevin Dynamics, through discrete and non-Markov diffusion processes, to continuous-time SDE/ODE formulations, specialized numerical solvers, and cutting-edge methods such as consistency models, distillation, and flow matching. Our goal is to provide both a historical perspective and a unified theoretical framework to help readers understand not only how these methods work but why they were developed.

• The Consistency Family: From Discrete-Time Constraints to Continuous-Time Flows

18 minute read

Published:

Consistency models (CMs) have recently emerged as a powerful paradigm for accelerating diffusion sampling by directly learning mappings that preserve consistency across noisy representations of the same data. This paper provides a comprehensive study of the Consistency Family, tracing its evolution from discrete consistency models to continuous-time formulations and trajectory-based extensions. We begin by revisiting the foundational motivation behind CMs and systematically derive their discrete and continuous objectives under both consistency distillation and consistency training paradigms.

Stability

• The Consistency Family: From Discrete-Time Constraints to Continuous-Time Flows

18 minute read

Published:

Consistency models (CMs) have recently emerged as a powerful paradigm for accelerating diffusion sampling by directly learning mappings that preserve consistency across noisy representations of the same data. This paper provides a comprehensive study of the Consistency Family, tracing its evolution from discrete consistency models to continuous-time formulations and trajectory-based extensions. We begin by revisiting the foundational motivation behind CMs and systematically derive their discrete and continuous objectives under both consistency distillation and consistency training paradigms.

• Diffusion Architectures Part II: Efficiency-Oriented Designs

57 minute read

Published:

Efficiency is a defining challenge for diffusion models, which often suffer from high computational cost and slow inference. This article surveys architectural strategies that enhance efficiency, from latent-space diffusion and multi-resolution cascades to lightweight convolutional blocks, efficient attention mechanisms, and parameter-efficient modules like LoRA. We also examine distillation and inference-time acceleration techniques that drastically reduce sampling steps. Together, these approaches demonstrate how architectural design can expand the reach of diffusion models — from research labs to real-time and mobile applications.

• Diffusion Architectures Part I: Stability-Oriented Designs

74 minute read

Published:

This article explores how network architectures shape the stability of diffusion model training. We contrast U-Net and Transformer-based (DiT) backbones, analyzing how skip connections, residual scaling, and normalization influence gradient propagation across noise levels. By surveying stability-oriented innovations such as AdaGN, AdaLN-Zero, and skip pathway regulation, we reveal why architectural choices can determine whether training converges smoothly or collapses. The discussion provides both theoretical insights and practical design rules for building robust diffusion models.

• Analysis of the Stability and Efficiency of Diffusion Model Training

73 minute read

Published:

while diffusion models have revolutionized generative AI, their training challenges stem from a combination of resource intensity, optimization intricacies, and deployment hurdles. A stable training process ensures that the model produces good quality samples and converges efficiently over time without suffering from numerical instabilities.

Stochastic Interpolants

• From Diffusion to Flow: A New Genrative Paradigm

33 minute read

Published:

In this post, we uncovered the foundations of Flow Matching: the limitations of diffusion models, the constraints of continuous flows, and the transformative idea of directly learning the path between distributions. From the intuition of Rectified Flow to the unifying lens of Stochastic Interpolants, Flow Matching emerged as more than a method — it is a paradigm that reframes generation as learning currents of transformation. With this conceptual map in hand, we are now ready to move from theory to practice.

Trajectory

• Inverse Problems with Generative Priors

49 minute read

Published:

📚 Table of Contents

• Flow Map Learning: A Unified Framework for Fast Generation

7 minute read

Published:

A “flow map” 1 2 3 typically denotes a neural network (or parametric model)

  1. Sabour A, Fidler S, Kreis K. Align Your Flow: Scaling Continuous-Time Flow Map Distillation[J]. arXiv preprint arXiv:2506.14603, 2025. ↩

  2. Boffi N M, Albergo M S, Vanden-Eijnden E. Flow map matching with stochastic interpolants: A mathematical framework for consistency models[J]. Transactions on Machine Learning Research, 2025. ↩

  3. Hu Z, Lai C H, Mitsufuji Y, et al. CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models[J]. arXiv preprint arXiv:2509.24526, 2025. ↩

Transformer

• Diffusion Architectures Part II: Efficiency-Oriented Designs

57 minute read

Published:

Efficiency is a defining challenge for diffusion models, which often suffer from high computational cost and slow inference. This article surveys architectural strategies that enhance efficiency, from latent-space diffusion and multi-resolution cascades to lightweight convolutional blocks, efficient attention mechanisms, and parameter-efficient modules like LoRA. We also examine distillation and inference-time acceleration techniques that drastically reduce sampling steps. Together, these approaches demonstrate how architectural design can expand the reach of diffusion models — from research labs to real-time and mobile applications.

• Diffusion Architectures Part I: Stability-Oriented Designs

74 minute read

Published:

This article explores how network architectures shape the stability of diffusion model training. We contrast U-Net and Transformer-based (DiT) backbones, analyzing how skip connections, residual scaling, and normalization influence gradient propagation across noise levels. By surveying stability-oriented innovations such as AdaGN, AdaLN-Zero, and skip pathway regulation, we reveal why architectural choices can determine whether training converges smoothly or collapses. The discussion provides both theoretical insights and practical design rules for building robust diffusion models.

UNET

• Diffusion Architectures Part II: Efficiency-Oriented Designs

57 minute read

Published:

Efficiency is a defining challenge for diffusion models, which often suffer from high computational cost and slow inference. This article surveys architectural strategies that enhance efficiency, from latent-space diffusion and multi-resolution cascades to lightweight convolutional blocks, efficient attention mechanisms, and parameter-efficient modules like LoRA. We also examine distillation and inference-time acceleration techniques that drastically reduce sampling steps. Together, these approaches demonstrate how architectural design can expand the reach of diffusion models — from research labs to real-time and mobile applications.

• Diffusion Architectures Part I: Stability-Oriented Designs

74 minute read

Published:

This article explores how network architectures shape the stability of diffusion model training. We contrast U-Net and Transformer-based (DiT) backbones, analyzing how skip connections, residual scaling, and normalization influence gradient propagation across noise levels. By surveying stability-oriented innovations such as AdaGN, AdaLN-Zero, and skip pathway regulation, we reveal why architectural choices can determine whether training converges smoothly or collapses. The discussion provides both theoretical insights and practical design rules for building robust diffusion models.

category1

• Controlled Generation with Diffusion Models

55 minute read

Published:

Over the past few years, controllable generation has become the central theme in the evolution of diffusion models. What began as a purely stochastic process for unconditional image synthesis has transformed into a programmable system capable of following text prompts, sketches, poses, depth maps, and even personalized identities. From Classifier-Free Guidance that amplifies conditional gradients, to Textual Inversion and DreamBooth that learn new concepts, to LoRA and ControlNet that extend controllability through lightweight adapters—each technique represents a different way of injecting intention into noise. This article traces the unifying logic behind these seemingly independent methods, revealing that all controllable diffusion approaches ultimately share a common goal: to reshape the diffusion trajectory so that generation obeys human-defined constraints while preserving creativity and diversity.

category2

• Controlled Generation with Diffusion Models

55 minute read

Published:

Over the past few years, controllable generation has become the central theme in the evolution of diffusion models. What began as a purely stochastic process for unconditional image synthesis has transformed into a programmable system capable of following text prompts, sketches, poses, depth maps, and even personalized identities. From Classifier-Free Guidance that amplifies conditional gradients, to Textual Inversion and DreamBooth that learn new concepts, to LoRA and ControlNet that extend controllability through lightweight adapters—each technique represents a different way of injecting intention into noise. This article traces the unifying logic behind these seemingly independent methods, revealing that all controllable diffusion approaches ultimately share a common goal: to reshape the diffusion trajectory so that generation obeys human-defined constraints while preserving creativity and diversity.

cool posts

• Controlled Generation with Diffusion Models

55 minute read

Published:

Over the past few years, controllable generation has become the central theme in the evolution of diffusion models. What began as a purely stochastic process for unconditional image synthesis has transformed into a programmable system capable of following text prompts, sketches, poses, depth maps, and even personalized identities. From Classifier-Free Guidance that amplifies conditional gradients, to Textual Inversion and DreamBooth that learn new concepts, to LoRA and ControlNet that extend controllability through lightweight adapters—each technique represents a different way of injecting intention into noise. This article traces the unifying logic behind these seemingly independent methods, revealing that all controllable diffusion approaches ultimately share a common goal: to reshape the diffusion trajectory so that generation obeys human-defined constraints while preserving creativity and diversity.