Acting in the world needs a model of it

Choice 1 — react. Look at the image, directly predict which block to pull.

Choice 2 — simulate. Model the tower's state → predict the outcome of each pull → pick the move that keeps it standing.

Interactive decisions require rolling out the consequences of actions — i.e. a world model you can query.

World model & the interactive loop

Interactive = the loop runs online: you act, it responds, you act again — fast, controllable, and stable over long horizons.

What an interactive world model needs

• Causal Streamable autoregressive roll-out — generate the future frame-by-frame, conditioned on the past.
• Controllable Respond to conditioning — text, images, actions, edits — without retraining a new model each time.
• Robust Stable over long horizons — no drift / error accumulation far beyond the training window.
• Real-time Few-step, low-latency generation so the loop can run interactively.
• Uncertainty Native density / likelihood — to score, plan, and detect the implausible.

We will revisit this scorecard at the end.

Today's video generators are mostly diffusion models

Powerful — but a few properties remain hard for the interactive setting (each is an active research area):

From diffusion to Normalizing Flows

A Normalizing Flow is a single invertible network $f$ mapping data $x$ to simple noise $z$.

Normalizing Flows in one slide

TARFlow — NFs are capable generative models

Transformer AR Flow. Stacked autoregressive Transformer blocks over patches, alternating scan direction.

Simple recipe — noise augmentation + post-hoc denoising + guidance → diffusion-level samples and SOTA likelihoods, from a stand-alone NF.

STARFlow — scaling latent NFs to high resolution

Deep–shallow design. One deep Transformer block carries most capacity + a few efficient shallow blocks.

Latent space. Model in a pretrained autoencoder's latent, not pixels — far more effective at high resolution.

+ new guidance, staying an end-to-end MLE flow. First NF at this scale/resolution, approaching diffusion quality.

STARFlow-V — the first NF video generator

Architecture: global–local

Why it may resist error accumulation

Efficiency: video-aware Jacobi iteration

Naive AR inversion decodes tokens one-by-one. Recast each flow block as a fixed-point system and sweep all tokens in parallel — converging in $k \ll N$ iterations, without breaking causality.

Jacobi iteration already achieves ~15× speedup over sequential AR decoding — but that still falls short of real-time interactive latency. Closing this gap is precisely the motivation for the next two works.

One model, three tasks — no fine-tuning

Quantitative: closing the gap to diffusion

Checkpoint — how far does STARFlow-V get us?

• ✓Causal streamable autoregressive roll-out.
• ✓Controllable T2V / I2V / V2V from one model.
• ✓Robust stable far past the training horizon.
• ✓Uncertainty native exact likelihood.
• ○Real-time Jacobi iteration gives ~15× speedup — but still not enough for interactive latency.

NFM — train as NF, test as flow matching

Like diffusion distillation — but using an AR-NF as the coupling oracle. A clean train / test separation:

NFM: inherit the coupling from an NF

Why it works — and beats OT

NFM: faster than the NF, and better

Can we do better? Enter NTM

NTM — text-to-image samples at 4 denoising steps (Fig 1)

Normalizing Trajectory Models (NTM) keep exact likelihood throughout — end-to-end, single training, and still sharp in as few as 4 steps.

The problem: Gaussian steps fail when coarse

Diffusion assumes each reverse step is a single small Gaussian. Compress to a few coarse steps and the true reverse $p(x_s\mid x_t)$ becomes a multimodal mixture — the Gaussian assumption breaks, so 4-step flow matching stays blurry.

Each step = an expressive conditional NF. The Gaussian assumption is replaced with a full NF transporter — model the true multimodal reverse exactly.

Where NTM sits: NF ↔ diffusion

NTM: a normalizing flow at each denoising step

Transporter $f_\mathcal{T}$ — shallow TarFlow-style NVP coupling blocks, applied within a single denoising step. Maps both $x_s$ and $x_t$ into a $u$-space where the conditional is Gaussian-simple.

Predictor $f_\mathcal{P}$ — deep full-attention Transformer, operates across the whole trajectory in parallel. Predicts the Gaussian mean and scale in $u$-space.

$\mathcal{L} = -\log p_\mathcal{P}(u_s \mid u_t) - \log\!\big|\det J_{f_\mathcal{T}}\big|$

Because $f_\mathcal{T}$ is invertible (not just a compressive encoder), this is the exact NLL of $p(x_s \mid x_t)$ — not a surrogate. Trained from scratch or initialized from any pretrained flow-matching model (set $f_\mathcal{T} = \mathrm{id}$).

Fast inference: trajectory denoising + learned denoiser

Step 1 — trajectory score denoising. The exact NTM likelihood gives a joint score over all timesteps. Its gradient (times the trajectory covariance) denoises the whole generated trajectory at once — no extra data needed.

Step 2 — post-train a lightweight denoiser $g_\phi$. Takes the cleanest predictor output $u_{t_0}$ → directly outputs $\hat x_0$. Trained with MSE against the score-denoised targets from the frozen NTM. Single forward pass at inference — no AR decoding, no backprop.

~9× speedup (0.20 → 1.88 img/s), LPIPS 0.121 vs score denoising. The base NTM's exact likelihood is what makes this distillation data-free and self-supervised.

NTM matches 50-step diffusion at 4 steps

Type	Model	GenEval↑	DPG↑
DM	SD3-Medium	0.62	84.08
DM	FLUX.1-dev	0.66	83.84
DM	Janus-Pro-7B	0.80	84.19
NF	STARFlow	0.56	—
NF	NTM (scratch, 256²)	0.82	79.64
NF	NTM (finetune FLUX, 512²)	0.76	83.38

From-scratch NTM at 4 steps outperforms FLUX.1-dev and matches Janus-Pro, while retaining exact likelihood. Finetuned NTM (from FLUX.2-klein 4B) closes further at 512².

Back to the question

• ✓Causal STARFlow-V: strict streamable autoregressive roll-out.
• ✓Controllable T2V / I2V / V2V from one invertible model, no fine-tuning.
• ✓Robust Stable to 30s — 6× past the training horizon.
• ✓Real-time NTM (4 steps) & NFM (up to 145×) attack latency — demonstrated on images; the path to video.
• ✓Uncertainty Exact density throughout — uniquely retained.

From images to the video world model

Open questions & future directions

Other work in this space

iTARFlow · ICML 2026
End-to-end NF with iterative diffusion-style denoising at sampling time — competitive ImageNet generation with exact likelihood training.

TARFlow-LM · NeurIPS 2025
Flexible patch-level AR flows for language — unified text generation via normalizing flows at the token-embedding level.

STARFlow2 · arXiv 2026
Pretzel 🥨 — a unified multimodal AR model bridging language models and NFs for image understanding, reasoning, and generation in one stream.

NF-CoT · coming soon
Latent reasoning with normalizing flows — continuous chain-of-thought inside an LLM backbone, with tractable likelihood enabling policy-gradient in thought space.