Towards Hierarchical Rectified Flow
Yichi Zhang, Yici Yan, Alex Schwing, Zhizhen Zhao
TL;DR
This paper introduces a hierarchical rectified flow model that captures complex data distributions more accurately by modeling multi-modal velocity and acceleration fields, resulting in more efficient data generation with fewer neural evaluations.
Contribution
It proposes a novel hierarchical rectified flow framework that models multi-modal velocity and acceleration fields, enabling intersecting integration paths and improved efficiency over classic rectified flows.
Findings
Fewer neural function evaluations needed for data generation.
Effective modeling of multi-modal data distributions.
Validated on synthetic and real datasets including ImageNet-32.
Abstract
We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data…
Peer Reviews
Decision·ICLR 2025 Poster
The strengths of the paper are listed below: - Clear motivation with well-written, easy-to-follow presentation. - Experimental results that partially support the theoretical claims.
The weaknesses of the paper are listed below: - While the paper's motivation is sound, my main concern lies in the practicality and application of the proposed approach. The generation framework demands significantly more model calls compared to the conventional RF framework, specifically NFEs multiplied by the number of discretizations in the velocity space. Although RF only targets mean velocity, it delivers strong empirical results with far greater efficiency than the proposed method. Additio
***Clarity and Accessibility***: The paper is well-written and presented in a logical manner, making the concepts and methodology easy to follow. Complex ideas are explained in a way that is accessible to readers with varying levels of familiarity with flow-based generative models, facilitating broader understanding and engagement with the research. ***Clear and Impactful Motivation***: The authors provide a compelling motivation for developing hierarchical rectified flow models, addressing lim
***Ambiguity in Extended Hierarchical Approach***: Although the acceleration-based approach and its motivation are clear and well-justified, the transition to the extended hierarchical flow model lacks clarity. Specifically, while the training objective for the acceleration-based approach is defined by Equation (8), the relationship to the hierarchical model’s training objective, outlined in Equation (10), is not thoroughly explained. The conceptual progression and the structural specifics of th
The paper is generally well written, even though a few parts could be improved. Theorem 1 and 2 are interesting results, and provide insights about the conditional distribution of velocities at each current point $x_t$ and they enable using higher order stochastic sampling.
My **main** concerns are the following: 1. The proposed method requires taking the position and the current velocity as input in order to predict the acceleration. The authors mention expanding the Resnet for their framework and increasing the amount of data processed. Can authors provide a detailed table comparing HRF and RF models, including parameter counts, training time per iteration, and memory usage across all experiments? 2. It is not clear if the NFE includes the steps required to sam
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Taxonomy
TopicsData Stream Mining Techniques · Simulation Techniques and Applications