The Föllmer process is a Brownian motion conditioned to have a pre-specified distribution at time 1. This process can be interpreted as an "augmented" time-compressed version of the reverse stochastic differential equation (SDE) for the denoising diffusion probabilistic model (DDPM). While this fact has been indirectly used to analyze DDPM sampling errors via discretization of the reverse SDE, connections between direct discretization of the Föllmer process and the DDPM sampler have not yet been fully explored. This note aims to clarify this point while surveying relevant results from existing work. We show that discretized Föllmer processes give natural hyper-parameter settings of the DDPM sampler. Moreover, this allows us to systematically recover state-of-the-art results on DDPM sampling error bounds with slight improvements.

This paper studies sampling error bounds for denoising diffusion probabilistic models (DDPMs) in the 2-Wasserstein distance. Our contributions are threefold. (i) Under general Lipschitz-type conditions on the score function and for a broad class of variance schedules, including the cosine schedule, we establish sharp upper bounds that are optimal in both the dimension and the number of steps, and recover several sharp error bounds previously obtained in the literature. (ii) We prove that the same Lipschitz-type conditions, which encompass those commonly imposed on the (learned) score, imply a logarithmic Sobolev inequality and hence a quadratic transportation cost inequality for the DDPM. As a consequence, in settings covered by existing work, an optimal Wasserstein bound, up to a logarithmic factor, follows from the recently obtained sharp error bound in the Kullback-Leibler divergence under geometric-type variance schedules. (iii) We show that for general log-concave target distributions, the optimal Wasserstein error bound remains attainable even without a quadratic transportation cost inequality for the target. Our analysis is based on viewing the DDPM sampler as a discretization of the Föllmer process rather than the conventional reverse Ornstein-Uhlenbeck process.

Representation Autoencoders (RAE) replace traditional VAE with pretrained vision encoders. In this paper, we systematically investigate several design choices and find three insights which simplify and improve RAE. First, we study a generalized formulation where the representation is defined as sum of the last k encoder layers rather than solely the final layer. This simple change greatly improves reconstruction without encoder finetuning or specialized data (e.g., text, faces). Second, we study the prevalent assumption that RAE (using pretrained representation as encoder) replaces representation alignment (REPA), which distills the same representation to intermediate layers instead. Through large-scale empirical analysis, we uncover a surprising finding: RAE and REPA exhibit complementary working mechanisms, allowing the same representation to be used as both encoder and target for intermediate diffusion layers. Finally, the original RAE struggles with classifier-free guidance (CFG) and requires training a second, weaker diffusion model for AutoGuidance (AG). We show that REPA itself can be viewed as x-prediction in RAE latent space. By simply re-parameterizing the output of the DiT model, it can provide guidance for "free". Overall, RAEv2 leads to more than 10x faster convergence over the original RAE, achieving a state-of-the-art gFID of 1.06 in just 80 epochs on ImageNet-256. On FDr^k, RAEv2 achieves a state-of-the-art 2.17 at just 80 epochs compared to the previous best 3.26 (800 epochs) without any post-training. This motivates EP_FID@k (epochs to reach unguided gFID <= k) as a measure of training efficiency. RAEv2 attains an EP_FID@2 of 35 epochs, versus 177 for the original RAE. We also validate our approach across diverse settings for text-to-image generation and navigation world models, showing consistent improvements. Code is available at https://raev2.github.io.

Pope Leo XIV holds the weekly general audience in St. Peter's Square at the Vatican on May 13. | REUTERS VATICAN CITY - Pope Leo will address the rise of artificial intelligence in his first in-depth text outlining his concerns, the Vatican said on Monday, adding that it would be unveiled on May 25 by the pontiff himself. The document, known as an encyclical, is likely to decry the use of AI in warfare and address how the technology is challenging workers' rights, according to sources. It will be titled "Magnifica Humanitas" (Magnificent Humanity) and was formally signed by the pope on Friday ahead of publication, a Vatican statement said. In a time of both misinformation and too much information, quality journalism is more crucial than ever. By subscribing, you can help us get the story right.

A new report alleges foreign influence from China, including state media and funded nonprofits like CodePink, is driving campaigns to block U.S. AI data center projects.

NextEra Energy is seeking to acquire Dominion Energy in an all-stock deal valued at about $67bn, creating a massive power company as the energy needs of artificial intelligence (AI) drive demand higher in the United States. It is one of the biggest proposed mergers so far this year and would create the world's largest regulated electric utility business by market capitalisation, the companies said on Monday. The region has a fast-growing population and the world's biggest data centre hub, which is in Virginia. The deal will enable a swifter build-out of power infrastructure to deliver electricity to data centres proposing to connect to NextEra and Dominion, which total about 130 gigawatts of electricity demand, the companies' executives said. One gigawatt can power about 750,000 homes. The merger builds on NextEra's efforts to tap into surging demand for supplying electricity to data centres developed by Big Tech, largely for training and rolling out AI technologies.

In its first week, the seventy-ninth edition of the festival unveiled standout new works by James Gray, Paweł Pawlikowski, and Ryûsuke Hamaguchi. Attend the Cannes Film Festival long enough, and you will grow wearily accustomed to the reality that some of the best films to première there are routinely overlooked for prizes. Lee Chang-dong magnificently unsettling psychological chiller, "Burning," failed to ignite the excitement of the 2018 jury. The tragicomic glories of Maren Ade's " Toni Erdmann," from 2016, were just as inexplicably unrewarded. Jurors shut out David Cronenberg's "A History of Violence," in 2005; Hou Hsiao-hsien's "Flowers of Shanghai," in 1998; Krzysztof Kieślowski's "Three Colors: Red," in 1994; Martin Scorsese's "Alice Doesn't Live Here Anymore," in 1975; and--the tradition goes way back--Vittorio De Sica's "Umberto D.," in 1952.

A United States jury has ruled against Elon Musk in his lawsuit against OpenAI, finding the artificial intelligence (AI) company not liable to the world's richest person for having allegedly strayed from its original mission to benefit humanity. In a unanimous verdict on Monday, the jury in Oakland, California US federal court said Musk had brought his case too late. Following the verdict, Musk's lawyer said he reserved the right to appeal, but the judge suggested he may have an uphill battle because whether the statute of limitations ran out before Musk sued was a factual issue. "There's a substantial amount of evidence to support the jury's finding, which is why I was prepared to dismiss on the spot," US District Judge Yvonne Gonzalez Rogers said. Musk was a co-founder of OpenAI, the company that launched in 2015 and went on to create ChatGPT.

Chiefs heiress Gracie Hunt might have set a bridesmaids record, fighting in the Dover parking lot & wings! Nothing to see here: Cowboys quarterback Dak Prescott and his ex's bridesmaid are just friends Can't sleep, Japanese bear-fighting robo-wolves will eat me and a gorilla trade captivates the nation A replica of KITT from'Knight Rider' got a traffic ticket in another state despite being in a museum Jena Sims covers her butt with a bow at the SI Swimsuit party, the NFL saves us from Romo & is Star Wars dead? Taylor Sheridan shocks'Yellowstone' fans with new spinoff series, provides viewers with dark ride Early reviews for new'Star Wars' movie are generally horrific, but does anyone even care at this point? Retired Navy admiral makes bombshell claim about UFOs and'non-human intelligence' controlling them Mother's Day chaos at a steakhouse includes knives thrown at waiters and a touching mother-daughter arrest Japanese bear-fightin' robo-wolves are pure unleaded nightmare fuel but they're working Trump-backed Gallrein blasts Massie as'misrepresentative,' defends record ahead of Kentucky primary Expert criticizes Iran's'illusion of diplomacy,' efforts to prolong conflict with US Dr. Ben Carson urges Americans to'stand up for what they believe in' after Rededicate 250 event Armando Salguero explains why everyone wins with the Steelers and Arron Rodgers deciding to join forces again for one more season. An area of Yangmingshan National Park, which is just north of Taipei in Taiwan, is getting a lot of attention after footage captured on a wildlife livestream went viral.

David Beckham and Dame Mary Berry are among the famous faces to have painted gnomes to raise funds for a school gardening campaign.