VDR and Diffusion: Zero-Drift Denoising Through Exact Sequential Arithmetic

Diffusion models generate images and video by iterating a denoising chain — each step takes the previous step's output, scales by schedule coefficients, subtracts predicted noise, normalizes, and feeds the result forward. In float64 arithmetic, each step introduces approximately 10⁻¹⁶ rounding error. Over 50 steps for image generation, this compounds to approximately 10⁻¹⁴. Over hundreds or thousands of steps for video generation, where frames condition on prior frames through the same arithmetic chain, the error produces measurable artifacts: color drift, temporal flickering, and structural inconsistency between frames. This paper implements the complete diffusion process — noise schedule computation, forward diffusion, reverse denoising, DDIM deterministic sampling, and multi-cycle drift measurement — in VDR exact integer arithmetic VDR-1. Every intermediate value is an exact rational number. Every operation preserves that exactness. The result: zero drift accumulation across arbitrarily long denoising chains. The error at cycle N equals the error at cycle 1, which is the Newton square root residual at the chosen depth (below 10⁻⁵⁰ at depth 10), not a compounding float truncation. Validated: 37 tests, 33 passed, 4 failed. All 4 failures trace to a normalization presentation issue — Newton iteration for perfect squares produces correct values that do not reduce to simplest form. Zero arithmetic errors. Zero drift. Zero computation failures. No prior reading is required. All necessary concepts from VDR arithmetic are introduced where first used.