Spherical Leech Quantization for Visual Tokenization and Generation
Non-parametric quantization has received much attention due to its efficiency on parameters and scalability to a large codebook. In this paper, we present a unified formulation of different non-parametric quantization methods through the lens of lattice coding. The geometry of lattice codes explains the necessity of auxiliary loss terms when training auto-encoders with certain existing lookup-free quantization variants such as BSQ. As a step forward, we explore a few possible candidates, including random lattices, generalized Fibonacci lattices, and densest sphere packing lattices. Among all, we find the Leech lattice-based quantization method, which is dubbed as Spherical Leech Quantization (Λ_{24}-SQ), leads to both a simplified training recipe and an improved reconstruction-compression tradeoff thanks to its high symmetry and even distribution on the hypersphere. In image tokenization and compression tasks, this quantization approach achieves better reconstruction quality across all metrics than BSQ, the best prior art, while consuming slightly fewer bits. The improvement also extends to state-of-the-art auto-regressive image generation frameworks.
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Yue Zhao
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2025-12-17T10:07:34.439Z
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Yue Zhao
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Hanwen Jiang
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Zhenlin Xu
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Chutong Yang
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Ehsan Adeli
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2025-12-17T10:12:37.792Z
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Ehsan Adeli
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user
eadeli42
694269a05d5b2dc105274a04
Philipp Krähenbühl
Spherical Leech Quantization for Visual Tokenization and Generation
Non-parametric quantization has received much attention due to its efficiency on parameters and scalability to a large codebook. In this paper, we present a unified formulation of different non-parametric quantization methods through the lens of lattice coding. The geometry of lattice codes explains the necessity of auxiliary loss terms when training auto-encoders with certain existing lookup-free quantization variants such as BSQ. As a step forward, we explore a few possible candidates, including random lattices, generalized Fibonacci lattices, and densest sphere packing lattices. Among all, we find the Leech lattice-based quantization method, which is dubbed as Spherical Leech Quantization (Λ_{24}-SQ), leads to both a simplified training recipe and an improved reconstruction-compression tradeoff thanks to its high symmetry and even distribution on the hypersphere. In image tokenization and compression tasks, this quantization approach achieves better reconstruction quality across all metrics than BSQ, the best prior art, while consuming slightly fewer bits. The improvement also extends to state-of-the-art auto-regressive image generation frameworks.
Lattice coding provides a unified framework for non-parametric quantization, with Leech lattice-based quantization achieving superior performance in image tokenization, compression, and generation tasks.
non-parametric quantization lattice coding auto-encoders BSQ random lattices generalized Fibonacci lattices densest sphere packing lattices Leech lattice Spherical Leech Quantization image tokenization compression auto-regressive image generation