Radiance field reconstruction aims to recover high-quality 3D representations from multi-view RGB images. Recent advances, such as 3D Gaussian splatting, enable real-time rendering with high visual fidelity on sufficiently powerful graphics hardware. However, efficient online transmission and rendering across diverse platforms requires drastic model simplification, reducing the number of primitives by several orders of magnitude. We introduce DiffSoup, a radiance field representation that employs a soup (i.e., a highly unstructured set) of a small number of triangles with neural textures and binary opacity. We show that this binary opacity representation is directly differentiable via stochastic opacity masking, enabling stable training without a mollifier (i.e., smooth rasterization). DiffSoup can be rasterized using standard depth testing, enabling seamless integration into traditional graphics pipelines and interactive rendering on consumer-grade laptops and mobile devices. Code is available at https://github.com/kenji-tojo/diffsoup.

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