Second, we show the first core-set w.r.t. the sum-of-nearest-neighbor distances. Finally, we run several experiments showing the effectiveness of our core-set approach. In particular, we apply constrained diversity maximization to summarize a set of timed messages that takes into account the messages' recency.

How the US left Ukraine exposed to Russia's winter war Will Europe use frozen Russian assets to fund war? How can Ukraine rebuild China ties? Three people were killed in a Russian drone attack on a civilian car in the city of Mykolaivka in the Kramatorsk district of Ukraine's Donetsk region, the state's emergency service said in a statement. The three people, as well as another person injured in the attack, were workers at the Sloviansk Thermal Power Station, the Kyiv Independent news outlet reported. A woman died after being injured in a Russian drone attack in Ukraine's Zaporizhia region, Governor Ivan Fedorov wrote on the Telegram messaging app.

Generating video stories from text prompts is a complex task. In addition to having high visual quality, videos need to realistically adhere to a sequence of text prompts whilst being consistent throughout the frames.

A.1 Proof of Proposition 4.1 Proposition 4.1 For any bounded measurable function τ(t): [0, T ] R, the following Reverse SDEs [ (1 + τ Eq. (20) is a reverse-time SDE running[ from T to 0, thus (there)are two additional minus ] signs in Eq. (21) before term A.2 Two Reparameterizations and Exact Solution under Exponential Integrator In this subsection, we will show the exact solution of SDE in both data prediction reparameterization and noise prediction reparameterization. The noise term in data prediction has smaller variance than noise prediction ones, implying the necessity of adopting data prediction reparameterization for the SDE sampler. The computation of variance uses the Itô Isometry, which is a crucial fact of Itô integral. Similar with Proposition 4.2, Eq. (37) can be solved analytically, which is shown in the following propositon: Following the derivation in Proposition 4.2, the mean of the Itô integral term is: [ A.2.4 Comparison between Data and Noise Reparameterizations In Table 1 we perform an ablation study on data and noise reparameterizations, the experiment results show that under the same magnitude of stochasticity, the proposed SA-Solver in data reparameterization has a better convergence which leads to better FID results under the same NFEs. In this subsection, we provide a theoretical view of this phenomenon.

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed.

To bridge this crucial gap, first, this paper presents a comprehensive benchmark suite to evaluate the out-of-distribution (OOD) performance of image compression methods.