# PhiZero: A World Model Built Around Physical Language > PHiZERO achieves state-of-the-art physical video generation and understanding by learning a compact discrete physical language for explicit transition reasoning before rendering. - **Source:** [arXiv](https://arxiv.org/abs/2607.28624) - **Published:** 2026-08-01 - **Permalink:** https://picx.dev/p/tKHGyr - **Whiteboard:** https://picx.dev/p/tKHGyr/image ## Summary ## Summary (Overview) - **PHIZERO** introduces a **physical language** – a compact discrete representation of state-transition patterns learned from unlabeled in-the-wild videos via self-supervised learning. - It adopts a **reason-then-render paradigm**: first infer future world evolution in physical-language space, then render the inferred transitions into videos. - Two core components: a **Physical Language Tokenizer** (encoder with transition-level Q‑Former + FSQ quantization + diffusion decoder) and a **Physical Language Reasoner** (autoregressive VLM predicting physical‑language sequences). - **Strong empirical results**: achieves top performance on physical video generation benchmarks (Physics‑IQ Verified, PhyGround, WorldModelBench) and competitive results on video understanding benchmarks (IntPhys2, LikePhys, YoCausal). - **Broader applications**: supports fine‑grained action‑conditioned simulation, interactive rollouts, and zero‑shot motion transfer across embodiments and visual domains. ## Introduction and Theoretical Foundation The paper is motivated by the observation that existing physical world models predict future videos directly in pixel space, leaving world dynamics implicit in high‑dimensional visual predictors. This often leads to physically inconsistent outcomes. Inspired by human intelligence – where patterns from visual experience are abstracted into generalizable knowledge and organized via natural language for explicit reasoning – the authors ask: *Can we learn a finer‑grained representation of physical‑world transitions that enables explicit reasoning?* The answer is **physical language**, a compact discrete representation of state‑transition patterns. Unlike natural language, which is too coarse for complex physical transitions, physical language captures the precise *how* of world evolution. PHIZERO is built around this representation: it reasons about world evolution in physical‑language space before rendering videos, separating dynamics inference from pixel synthesis. ## Methodology ### Problem Formulation Let \(V\) be the future video, \(I_0\) the first frame, \(c\) the textual action intent, and \(z\) the discrete physical language describing the transition from \(I_0\) to \(V\). The prediction factorizes as: $$ p_{\theta,\psi}(V, z \mid I_0, c) = p_{\theta}(z \mid I_0, c) \; p_{\psi}(V \mid I_0, z) $$ where \(\theta\) is the Physical Language Reasoner and \(\psi\) the diffusion decoder (Eq. 1). ### Physical Language Tokenizer - **Encoder with Transition‑level Q‑Former**: A spatiotemporal encoder extracts latent features. For each adjacent pair of latent states \((x_i, x_{i+1})\), a shared Q‑Former with \(M\) learnable queries extracts transition features \(q_i\) (Eq. 2). These are concatenated and quantized via **FSQ** (Finite Scalar Quantization) to obtain the discrete physical‑language sequence \(z\) (Eq. 3): $$ z = \text{FSQ}(\text{Proj}_{\text{down}}(q)) $$ - **Diffusion‑prior Decoder**: A pretrained video diffusion model (Wan2.2‑5B) is used as decoder. Only the text condition is replaced with the physical‑language context \(P_c\). The first frame \(I_0\) provides static appearance, encouraging the bottleneck to encode only state transitions. The decoder is fine‑tuned with LoRA using the flow‑matching objective (Eq. 4): $$ \mathcal{L}_{\text{FM}} = \mathbb{E}_{x,\epsilon,\tau}\left[\left\| v_{\psi}(x_\tau, \tau; I_0, P_c) - (\epsilon - x_0) \right\|_2^2\right], \quad x_\tau = (1-\tau)x_0 + \tau\epsilon $$ - **Pure‑noise Warm‑up**: To prevent the decoder from ignoring the physical‑language context, future frames are initialized from pure noise in a warm‑up stage, forcing reliance on the physical‑language condition. - **Data curation**: A hierarchical pipeline yields 10K hours for pretraining, 5M 4‑second clips for tokenizer SFT, and 1M motion‑rich clips for reasoner SFT. A curriculum progresses from 256×448 resolution and 1s clips to 512×896 and 4s. ### Physical Language Reasoner - **Architecture**: Initialized from a pretrained VLM (Qwen3‑VL‑4B) with vocabulary extended to include one atomic symbol per FSQ index (25K symbols). It autoregressively predicts a length‑\(N\) physical‑language sequence \(z\) (Eq. 5): $$ p_\theta(z \mid I_0, c) = \prod_{j=1}^{N} p_\theta(z_j \mid I_0, c, z_{