# RectifID: Personalizing Rectified Flow with Anchored Classifier Guidance

## ๐ Abstract

The paper proposes a training-free approach to flexibly personalize rectified flow models using anchored classifier guidance. It extends the applicability of the original classifier guidance by transforming it into a new fixed-point formulation that can leverage off-the-shelf image discriminators, without relying on a special noise-aware classifier. To improve the stability of this fixed-point solution, the paper introduces an anchored classifier guidance that constrains the target flow trajectory to be close to a reference trajectory, providing a theoretical convergence guarantee. The derived method is implemented on a practical class of piecewise rectified flow and demonstrates advantageous results in various personalization tasks for human faces, live subjects, certain objects, and multiple subjects.

## ๐ Q&A

### [01] Classifier Guidance for Rectified Flow

**1. What is the key observation that allows bypassing the need for a noise-aware classifier?**
The key observation is that by approximating the rectified flow trajectory to be ideally straight, the original classifier guidance can be reformulated as a simple fixed-point problem involving only the trajectory endpoints, without requiring the noise-aware classifier.

**2. What is the limitation of the initial fixed-point solution derived based on this observation?**
The initial fixed-point solution may not always converge, as even a small perturbation at the starting point could lead to the target flow trajectory diverging significantly after iterative updates, hindering the controllability of the rectified flow.

**3. How does the paper address this limitation?**
To improve the stability, the paper proposes a new "anchored classifier guidance" that constrains the target flow trajectory to be close to a predetermined reference trajectory. This provides a better convergence guarantee and a certain degree of interpretability.

### [02] Anchored Classifier Guidance

**1. What is the key idea behind the anchored classifier guidance?**
The key idea is to constrain the target flow trajectory to be straight and near a reference trajectory, by anchoring the target velocity to the reference velocity. This helps stabilize the solving process of the target trajectory.

**2. How does the anchored classifier guidance bypass the need for a noise-aware classifier?**
Similar to the initial fixed-point solution, the anchored classifier guidance substitutes the intermediate classifier guidance terms with an expression involving only the trajectory endpoints, allowing the use of off-the-shelf image discriminators.

**3. What theoretical property does the anchored classifier guidance exhibit?**
The paper shows that the fixed-point iteration to solve the anchored classifier guidance exhibits at least linear convergence, provided that the image discriminator is Lipschitz continuous, by properly choosing the guidance scale.

### [03] Practical Algorithm

**1. How does the paper extend the analysis to handle practical rectified flow models?**
The paper relaxes the assumption of an ideally straight rectified flow trajectory, and instead adopts a piecewise linear approximation, where the flow trajectory is assumed straight within each time window.

**2. How does the paper address the issue of disconnected reference trajectory segments after updates?**
To handle the disconnected reference trajectory segments, the paper proposes to reinitialize the reference trajectory every iteration with predictions for the updated target starting points.

**3. What are the key steps in the iterative procedure to solve the target flow trajectory under the anchored classifier guidance?**
The key steps are: 1) Predict the updated target starting points by extrapolating from history updates; 2) Solve the derived fixed-point problem to obtain the new target trajectory, anchored to the reinitialized reference trajectory.

### [04] Applications

**1. What types of personalization tasks does the proposed method cover?**
The proposed method is flexible for various personalized image generation tasks, including human faces, live subjects (e.g. cats, dogs), certain objects (e.g. cans, vases), and even multiple subjects.

**2. How does the method leverage off-the-shelf image discriminators for these tasks?**
For face-centric personalization, the method uses a face specialist discriminator (ArcFace). For subject-driven generation, it employs an open-vocabulary object detector (OWL-ViT) and a self-supervised backbone (DINOv2) to extract visual features.

**3. How does the method handle the multi-subject scenario?**
The method extends to the multi-subject case by incorporating a bipartite matching step to associate the generated subjects with the reference subjects, before computing the classifier guidance signal.

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