$$ \def\ba{\mathbf{a}} \def\bb{\mathbf{b}} \def\bc{\mathbf{c}} \def\bd{\mathbf{d}} \def\be{\mathbf{e}} \def\bf{\mathbf{f}} \def\bg{\mathbf{g}} \def\bh{\mathbf{h}} \def\bi{\mathbf{i}} \def\bj{\mathbf{j}} \def\bk{\mathbf{k}} \def\bl{\mathbf{l}} \def\bm{\mathbf{m}} \def\bn{\mathbf{n}} \def\bo{\mathbf{o}} \def\bp{\mathbf{p}} \def\bq{\mathbf{q}} \def\br{\mathbf{r}} \def\bs{\mathbf{s}} \def\bt{\mathbf{t}} \def\bu{\mathbf{u}} \def\bv{\mathbf{v}} \def\bw{\mathbf{w}} \def\bx{\mathbf{x}} \def\by{\mathbf{y}} \def\bz{\mathbf{z}} \def\bA{\mathbf{A}} \def\bB{\mathbf{B}} \def\bC{\mathbf{C}} \def\bD{\mathbf{D}} \def\bE{\mathbf{E}} \def\bF{\mathbf{F}} \def\bG{\mathbf{G}} \def\bH{\mathbf{H}} \def\bI{\mathbf{I}} \def\bJ{\mathbf{J}} \def\bK{\mathbf{K}} \def\bL{\mathbf{L}} \def\bM{\mathbf{M}} \def\bN{\mathbf{N}} \def\bO{\mathbf{O}} \def\bP{\mathbf{P}} \def\bQ{\mathbf{Q}} \def\bR{\mathbf{R}} \def\bS{\mathbf{S}} \def\bT{\mathbf{T}} \def\bU{\mathbf{U}} \def\bV{\mathbf{V}} \def\bW{\mathbf{W}} \def\bX{\mathbf{X}} \def\bY{\mathbf{Y}} \def\bZ{\mathbf{Z}} \def\balpha{\boldsymbol{\alpha}} \def\bbeta{\boldsymbol{\beta}} \def\bgamma{\boldsymbol{\gamma}} \def\bdelta{\boldsymbol{\delta}} \def\bepsilon{\boldsymbol{\epsilon}} \def\bvarepsilon{\boldsymbol{\varepsilon}} \def\bzeta{\boldsymbol{\zeta}} \def\btheta{\boldsymbol{\theta}} \def\bvartheta{\boldsymbol{\vartheta}} \def\biota{\boldsymbol{\iota}} \def\bkappa{\boldsymbol{\kappa}} \def\blambda{\boldsymbol{\lambda}} \def\bmu{\boldsymbol{\mu}} \def\bnu{\boldsymbol{\nu}} \def\bxi{\boldsymbol{\xi}} \def\bpi{\boldsymbol{\pi}} \def\brho{\boldsymbol{\rho}} \def\bsigma{\boldsymbol{\sigma}} \def\bvarsigma{\boldsymbol{\varsigma}} \def\btau{\boldsymbol{\tau}} \def\bupsilon{\boldsymbol{\upsilon}} \def\bphi{\boldsymbol{\phi}} \def\bvarphi{\boldsymbol{\varphi}} \def\bchi{\boldsymbol{\chi}} \def\bpsi{\boldsymbol{\psi}} \def\bomega{\boldsymbol{\omega}} \def\bGamma{\boldsymbol{\Gamma}} \def\bDelta{\boldsymbol{\Delta}} \def\bTheta{\boldsymbol{\Theta}} \def\bLambda{\boldsymbol{\Lambda}} \def\bXi{\boldsymbol{\Xi}} \def\bPi{\boldsymbol{\Pi}} \def\bSigma{\boldsymbol{\Sigma}} \def\bUpsilon{\boldsymbol{\Upsilon}} \def\bPhi{\boldsymbol{\Phi}} \def\bPsi{\boldsymbol{\Psi}} \def\bOmega{\boldsymbol{\Omega}} \def\bba{\mathbb{a}} \def\bbb{\mathbb{b}} \def\bbc{\mathbb{c}} \def\bbd{\mathbb{d}} \def\bbe{\mathbb{e}} \def\bbf{\mathbb{f}} \def\bbg{\mathbb{g}} \def\bbh{\mathbb{h}} \def\bbi{\mathbb{i}} \def\bbj{\mathbb{j}} \def\bbk{\mathbb{k}} \def\bbl{\mathbb{l}} \def\bbm{\mathbb{m}} \def\bbn{\mathbb{n}} \def\bbo{\mathbb{o}} \def\bbp{\mathbb{p}} \def\bbq{\mathbb{q}} \def\bbr{\mathbb{r}} \def\bbs{\mathbb{s}} \def\bbt{\mathbb{t}} \def\bbu{\mathbb{u}} \def\bbv{\mathbb{v}} \def\bbw{\mathbb{w}} \def\bbx{\mathbb{x}} \def\bby{\mathbb{y}} \def\bbz{\mathbb{z}} \def\bbA{\mathbb{A}} \def\bbB{\mathbb{B}} \def\bbC{\mathbb{C}} \def\bbD{\mathbb{D}} \def\bbE{\mathbb{E}} \def\bbF{\mathbb{F}} \def\bbG{\mathbb{G}} \def\bbH{\mathbb{H}} \def\bbI{\mathbb{I}} \def\bbJ{\mathbb{J}} \def\bbK{\mathbb{K}} \def\bbL{\mathbb{L}} \def\bbM{\mathbb{M}} \def\bbN{\mathbb{N}} \def\bbO{\mathbb{O}} \def\bbP{\mathbb{P}} \def\bbQ{\mathbb{Q}} \def\bbR{\mathbb{R}} \def\bbS{\mathbb{S}} \def\bbT{\mathbb{T}} \def\bbU{\mathbb{U}} \def\bbV{\mathbb{V}} \def\bbW{\mathbb{W}} \def\bbX{\mathbb{X}} \def\bbY{\mathbb{Y}} \def\bbZ{\mathbb{Z}} \def\cA{\mathcal{A}} \def\cB{\mathcal{B}} \def\cC{\mathcal{C}} \def\cD{\mathcal{D}} \def\cE{\mathcal{E}} \def\cF{\mathcal{F}} \def\cG{\mathcal{G}} \def\cH{\mathcal{H}} \def\cI{\mathcal{I}} \def\cJ{\mathcal{J}} \def\cK{\mathcal{K}} \def\cL{\mathcal{L}} \def\cM{\mathcal{M}} \def\cN{\mathcal{N}} \def\cO{\mathcal{O}} \def\cP{\mathcal{P}} \def\cQ{\mathcal{Q}} \def\cR{\mathcal{R}} \def\cS{\mathcal{S}} \def\cT{\mathcal{T}} \def\cU{\mathcal{U}} \def\cV{\mathcal{V}} \def\cW{\mathcal{W}} \def\cX{\mathcal{X}} \def\cY{\mathcal{Y}} \def\cZ{\mathcal{Z}} \def\ta{\textnormal{a}} \def\tb{\textnormal{b}} \def\tc{\textnormal{c}} \def\td{\textnormal{d}} \def\te{\textnormal{e}} \def\tf{\textnormal{f}} \def\tg{\textnormal{g}} \def\th{\textnormal{h}} \def\ti{\textnormal{i}} \def\tj{\textnormal{j}} \def\tk{\textnormal{k}} \def\tl{\textnormal{l}} \def\tm{\textnormal{m}} \def\tn{\textnormal{n}} \def\to{\textnormal{o}} \def\tp{\textnormal{p}} \def\tq{\textnormal{q}} \def\tr{\textnormal{r}} \def\ts{\textnormal{s}} \def\tt{\textnormal{t}} \def\tu{\textnormal{u}} \def\tv{\textnormal{v}} \def\tw{\textnormal{w}} \def\tx{\textnormal{x}} \def\ty{\textnormal{y}} \def\tz{\textnormal{z}} \def\tA{\textnormal{A}} \def\tB{\textnormal{B}} \def\tC{\textnormal{C}} \def\tD{\textnormal{D}} \def\tE{\textnormal{E}} \def\tF{\textnormal{F}} \def\tG{\textnormal{G}} \def\tH{\textnormal{H}} \def\tI{\textnormal{I}} \def\tJ{\textnormal{J}} \def\tK{\textnormal{K}} \def\tL{\textnormal{L}} \def\tM{\textnormal{M}} \def\tN{\textnormal{N}} \def\tO{\textnormal{O}} \def\tP{\textnormal{P}} \def\tQ{\textnormal{Q}} \def\tR{\textnormal{R}} \def\tS{\textnormal{S}} \def\tT{\textnormal{T}} \def\tU{\textnormal{U}} \def\tV{\textnormal{V}} \def\tW{\textnormal{W}} \def\tX{\textnormal{X}} \def\tY{\textnormal{Y}} \def\tZ{\textnormal{Z}} \newcommand{\defeq}{\overset{\text{def}}{=}} \newcommand{\smallR}{\mbox{\tiny R}} \newcommand{\smallF}{\mbox{\tiny F}} \newcommand{\softmax}{\mathrm{softmax}} \newcommand{\sigmoid}{\sigma} \newcommand{\KL}{D_{\mathrm{KL}}} \newcommand{\Var}{\mathrm{Var}} \newcommand{\Cov}{\mathrm{Cov}} $$

Beyond Scale: Embodied Generalization Is a State Representation Problem

July 9, 2026

Current embodied models, including recent VLAs (Vision-Language-Action models), still struggle when deployed in unseen environments or on unseen embodiments. They often look robust in benchmark settings, but fail once scene layout, object set, camera viewpoint, control frequency, or robot kinematics shift.

The Essence of Bayesian Flow Networks

September 20, 2024

For easy understanding, the reader can treat the variables as discrete variables. Without loss of generality, the formulation can be easily extended to continuous variables by swapping the summation with integration. This post introduces the Bayesian Flow Networks¹ (BFN) in a more simple language.

Alex Graves, Rupesh Kumar Srivastava, Timothy Atkinson, Faustino Gomez. “Bayesian flow networks”, arXiv 2023. ↩