Tokenize the Physics, Not the Pixels: TessTok and Fold-Flow Quantization for Material Microstructures

Visual tokenizers compress images into the tokens that latent generative models learn from. Existing tokenizers are built for natural images: a fixed latent grid, a codebook or straight-through estimator, and a perceptual objective. A physical field is instead a set of objects that a simulation reads directly. *Can a discrete tokenizer compress a material microstructure field by two orders of magnitude and return a field a crystal-plasticity solver can run?* We present **TessTok**, which encodes a polycrystal as sparse quantized Laguerre grain seeds and regrows it deterministically. Its **Fold-Flow Quantizer (FFQ)** needs no codebook or straight-through estimator and learns where to place its levels. At $10.4$ kbit per $256\times 256$ field reconstruction, TessTok reaches $24.4$ dB and $8.9$ rFID and matches $93\%$ of the grains, against $22.1$ dB, $45.1$ and $69$ for ViT-VQGAN at $13.3$ kbit. At matched bits, FFQ beats every codebook and binary quantizer on all pixel and orientation metrics with no codebook to collapse. TessTok also keeps $90\%$ of grain area at $4.4$ kbit, below the rate of MAGVIT-v2. On ImageNet, with its grain-specific parts switched off, the same code gives the highest PSNR among the latest tokenizers, though not the best perceptual scores and compression rate. Tokenizing physical-object fields instead of pixels, lets our model work at many bit budgets, and lets a reconstruction be governed by the physical simulation needs.