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Dogyun Park, Sojin Lee, Sihyeon Kim, Taehoon Lee, Youngjoon Hong, Hyunwoo J. Kim†

Constant Acceleration Flow

Machine Learning and Vision Lab

Computer Science and Engineering

Korea University

1

Korea University

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Preliminary: Rectified Flow

 

 

 

 

 

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Preliminary: Rectified Flow

 

 

 

 

 

 

Single-step generation!

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Preliminary: Rectified Flow

✔︎ Simulation-free training framework.

 

 

 

 

 

 

 

 

 

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Preliminary: Rectified Flow

✔︎ Simulation-free training framework.

 

 

 

 

 

 

 

 

 

 

 

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Preliminary: Rectified Flow

✔︎ Flow crossing

 

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Preliminary: Rectified Flow

✔︎ Flow crossing

✔︎ Reflow procedure

  • Use a pre-trained model (e.g., 1-Rectified Flow) to generate deterministic coupling.

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  • Train 2-Rectified Flow on the generated deterministic coupling.

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  • The reflow procedure has been shown to straighten trajectories, improving single-step generation.

 

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Preliminary: Rectified Flow

✔︎ Limitations

  • Problem 1. Relying solely on velocity to estimate complex transformations between distributions may restrict expressivity and limit the model’s performance.

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  • Problem 2. Despite reflow, flow crossings can still occur, resulting in suboptimal outcomes for single-step sampling.

Results of 2-Rectified Flow (N=2) on 2D synthetic data.

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Method: Constant Acceleration Flow

✔︎ Constant Acceleration Flow Ordinary Differential Equation (ODE)

 

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Method: Constant Acceleration Flow

✔︎ Constant Acceleration Flow Ordinary Differential Equation (ODE)

 

Single-step sampling!

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Method: Constant Acceleration Flow

✔︎ Constant Acceleration Flow Ordinary Differential Equation (ODE)

 

Single-step sampling!

 

Rectified flow sampling

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Method: Constant Acceleration Flow

✔︎ Constant Acceleration Flow Ordinary Differential Equation (ODE)

 

 

Single-step sampling!

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Method: Constant Acceleration Flow

✔︎ Constant Acceleration Flow Ordinary Differential Equation (ODE)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Method: Constant Acceleration Flow

 

 

 

 

 

 

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Method: Constant Acceleration Flow

✔︎ Flow dynamics of CAF ODE

 

(A)

(B)

(C)

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Method: Constant Acceleration Flow

✔︎ Addressing flow crossing problem

  • Initial Velocity Conditioning (IVC)

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< Without IVC >

< With IVC >

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Method: Constant Acceleration Flow

✔︎ Overall training pipeline

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Method: Constant Acceleration Flow

✔︎ Sampling

✔︎ Inversion

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Experiments: 2D-Toy

2-Rectified Flow (N=2)

CAF (ours) h=2

CAF (ours) h=1

CAF (ours) h=0.5

✔︎ Results on 2D Gaussian mixture distribution

  • CAF clearly demonstrate more accurate single-step generation compared to Rectified Flow.

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Experiments: Real-data Experiments

✔︎ Results on Cifar-10 and ImageNet 64x64

  • Achieves better or comparable performance compared to state-of-the-art models.

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Experiments: Qualitative results

✔︎ Qualitative results on Cifar-10

  • CAF clearly generates more vivid and realistic images compared to Rectified Flow.

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Analysis: Ablation study

✔︎ Ablation study on Cifar-10

  • Config (B) vs. Config (C) demonstrates effectiveness of constant acceleration modeling.

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  • Config (C) vs. Config (D) demonstrates effectiveness of IVC.

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Analysis: Coupling Preservation

✔︎ Property of CAF

 

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Analysis: Few-step Inversion

✔︎ Property of CAF

Ground Truth

Reconstruction (N=1)

  • CAF also demonstrates accurate single-step reconstruction using inversion, making it highly efficient for real-world applications such as image editing.

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Analysis: Zero-shot box Inpainting

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Conclusion

  • Constant Acceleration Flow (CAF) introduces a novel ODE framework, enhancing Rectified Flow with a constant acceleration term for improved accuracy.

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  • We introduce two additional techniques, Initial Velocity Conditioning (IVC) and reflow for initial velocity, effectively addressing the flow-crossing problem.

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  • CAF demonstrates superior performance in single-step generation, highlighting its efficacy and efficiency.

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  • With excellent coupling preservation and efficient few-step inversion, CAF is highly suitable for practical applications, such as image editing, where precision and speed are essential.

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Thank you.

Github

Paper

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