Score normalization for a faster diffusion exponential integrator sampler

Recently, Zhang and Chen [25] have proposed the Diffusion Exponential Integrator Sampler (DEIS) for fast generation of samples from Diffusion Models. It leverages the semi-linear nature of the probability flow ordinary differential equation (ODE) in order to greatly reduce integration error and improve generation quality at low numbers of function evaluations (NFEs). Key to this approach is the score function reparameterisation, which reduces the integration error incurred from using a fixed score function estimate over each integration step. The original authors use the default parameterisation used by models trained for noise prediction – multiply the score by the standard deviation of the conditional forward noising distribution. We find that although the mean absolute value of this score parameterisation is close to constant for a large portion of the reverse sampling process, it changes rapidly at the end of sampling. As a simple fix, we propose to instead reparameterise the score (at inference) by dividing it by the average absolute value of previous score estimates at that time step collected from offline high NFE generations. We find that our score normalisation (DEIS-SN) consistently improves FID compared to vanilla DEIS, showing an improvement at 10 NFEs from 6.44 to 5.57 on CIFAR-10 and from 5.9 to 4.95 on LSUN-Church (64×64). Our code is available at https://github.com/mtkresearch/Diffusion-DEIS-SN.<br/

SIGMA: spectral interpretation using gaussian mixtures and autoencoder

Identification of unknown micro- and nano-sized mineral phases is commonly achieved by analyzing chemical maps generated from hyperspectral imaging data sets, particularly scanning electron microscope—energy dispersive X-ray spectroscopy (SEM-EDS). However, the accuracy and reliability of mineral identification are often limited by subjective human interpretation, non-ideal sample preparation, and the presence of mixed chemical signals generated within the electron-beam interaction volume. Machine learning has emerged as a powerful tool to overcome these problems. Here, we propose a machine-learning approach to identify unknown phases and unmix their overlapped chemical signals. This approach leverages the guidance of Gaussian mixture modeling clustering fitted on an informative latent space of pixel-wise elemental data points modeled using a neural network autoencoder, and unmixes the overlapped chemical signals of phases using non-negative matrix factorization. We evaluate the reliability and the accuracy of the new approach using two SEM-EDS data sets: a synthetic mixture sample and a real-world particulate matter sample. In the former, the proposed approach successfully identifies all major phases and extracts background-subtracted single-phase chemical signals. The unmixed chemical spectra show an average similarity of 83.0% with the ground truth spectra. In the second case, the approach demonstrates the ability to identify potentially magnetic Fe-bearing particles and their background-subtracted chemical signals. We demonstrate a flexible and adaptable approach that brings a significant improvement to mineralogical and chemical analysis in a fully automated manner. The proposed analysis process has been built into a user-friendly Python code with a graphical user interface for ease of use by general users

Score Normalization for a Faster Diffusion Exponential Integrator Sampler

Recently, Zhang et al. have proposed the Diffusion Exponential Integrator Sampler (DEIS) for fast generation of samples from Diffusion Models. It leverages the semi-linear nature of the probability flow ordinary differential equation (ODE) in order to greatly reduce integration error and improve generation quality at low numbers of function evaluations (NFEs). Key to this approach is the score function reparameterisation, which reduces the integration error incurred from using a fixed score function estimate over each integration step. The original authors use the default parameterisation used by models trained for noise prediction -- multiply the score by the standard deviation of the conditional forward noising distribution. We find that although the mean absolute value of this score parameterisation is close to constant for a large portion of the reverse sampling process, it changes rapidly at the end of sampling. As a simple fix, we propose to instead reparameterise the score (at inference) by dividing it by the average absolute value of previous score estimates at that time step collected from offline high NFE generations. We find that our score normalisation (DEIS-SN) consistently improves FID compared to vanilla DEIS, showing an improvement at 10 NFEs from 6.44 to 5.57 on CIFAR-10 and from 5.9 to 4.95 on LSUN-Church 64x64. Our code is available at https://github.com/mtkresearch/Diffusion-DEIS-S

Segregation of anion (Cl−) impurities at transparent polycrystalline α-alumina interfaces

Small amounts of anion impurities (e.g. Cl), which are incorporated during the synthesis of ceramic powders, can affect the properties and microstructure of the final sintered ceramic. The effect of anion impurities is a little studied and poorly understood phenomenon. In this work a combination of STEM-EDX analysis and atomistic modeling approach was used to understand the segregation of Cl in transparent alumina ceramics. A high resolution analytical electron microscopy study showed the presence of Cl at the grain boundaries and especially at triple points. Atomistic simulations were carried out to understand the origins and consequences of such segregation. Segregation energy calculations predict a strong segregation of Cl at the different surfaces and grain boundaries of alumina. A higher coordination number of Cl at surfaces was observed, which indicates strong ionic bonds making it difficult to remove at low temperature, which explains the presence of Cl at triple points

Image generation with shortest path diffusion

The field of image generation has made significant progress thanks to the introduction of Diffusion Models, which learn to progressively reverse a given image corruption. Recently, a few studies introduced alternative ways of corrupting images in Diffusion Models, with an emphasis on blurring. However, these studies are purely empirical and it remains unclear what is the optimal procedure for corrupting an image. In this work, we hypothesize that the optimal procedure minimizes the length of the path taken when corrupting an image towards a given final state. We propose the Fisher metric for the path length, measured in the space of probability distributions. We compute the shortest path according to this metric, and we show that it corresponds to a combination of image sharpening, rather than blurring, and noise deblurring. While the corruption was chosen arbitrarily in previous work, our Shortest Path Diffusion (SPD) determines uniquely the entire spatiotemporal structure of the corruption. We show that SPD improves on strong baselines without any hyperparameter tuning, and outperforms all previous Diffusion Models based on image blurring. Furthermore, any small deviation from the shortest path leads to worse performance, suggesting that SPD provides the optimal procedure to corrupt images. Our work sheds new light on observations made in recent works and provides a new approach to improve diffusion models on images and other types of data.Comment: AD and SF contributed equall

From 2D to 3D Characterization of Materials Subjected to Extreme Pressure and Temperature Conditions

Planetesimal were the first planetary objects to form in the solar system, which later grew to make the proto-planets. Most of these bodies were differentiated as a result of internal heating. Several differentiated bodies have, then, been accreted following the giant impacts to create the terrestrial planets. As a result of these impacts, the newly formed Earth was molten and completely differentiated. Subsequent crystallization has given rise to Earth's current structure. In order to bring new constraints on the differentiation and melting relationship in the planets we have studied natural and synthetic samples corresponding to different stages of planetary evolution through state of the art electron microscopy techniques. We have, first, looked at carbonaceous materials in a ureilite meteorite (Almahata Sitta MS-170). Thin sections from ureilite diamonds were prepared with the focused ion beam (FIB) are observed by transmission electron microscopy and spectroscopy. The morphology of graphite bands in diamonds indicated that they result from the diamond to graphite transformation during a shock event. Moreover, the diamonds in this meteorite with crystallite sizes as large as ~20 ÎŒm can only form under static high-pressure condition of planetary interiors. We have, also, found three types of diamond inclusions in our samples. The majority of these inclusions are euhedral Fe-S inclusions. However, each of these inclusions has three phases, namely: kamacite (Fe, Ni), troilite (FeS), and schreibersite ((Fe, Ni)3 P). The chemical analysis of the intact inclusions shows them to be a stoichiometric phase, (Fe, Ni)3(S, P), that can only form above 21 GPa. The ureilite parent body (UPB) should have had the size about that of Mars to exert necessary pressure to grow the diamond inclusions in the core-mantle boundary. The other two types of inclusions are the Al- and Mg- free chromite, Cr2FeO4, and Ca-Fe phosphates that were previously observed only in iron meteorites. Our results suggest that the diamonds and their inclusions were formed from an S-rich metallic liquid. In the second part of the thesis, we have studied melting and fractional crystallization of the lower mantle using a laser-heated diamond anvil cell (LH-DAC). San Carlos olivine is used as a proxy to the mantle composition. The recovered samples are first analyzed with the 3D chemical tomography using a dual beam FIB instrument. The molten region in all the samples at pressure range from 30 to 71 GPa have at least three distinct zones: a ferropericlase shell (Fp), an intermediate bridgmanite (Brg) region and the Fe-rich melt core. Thin sections from the center of the same samples are analyzed with TEM and energy-dispersive x-ray (EDX) spectroscopy. The results from the samples heated at 45 GPa for 1, 3, and 6 minutes demonstrated that the temperature gradient in the heated zone shrinks through the time and, thus, the crystallization continues toward the center of the heating. Consequently, the melt becomes richer in iron. The melt core also gets more iron-rich with increasing pressure. In fact, in ~70 GPa we observe an Fe-O core with small Si and Mg concentration. This implies that the melt at the bottom of the mantle could become denser than the solid phases and sink down. The presence of the iron-rich melt or the oxides crystallizing from such a melt can explain the ultra-low velocity zones (ULVZs) found in the seismic surveys of the core-mantle boundary

SIGMA: Spectral Interpretation using Gaussian Mixtures and Autoencoder

Identification of unknown micro- and nano-sized mineral phases is commonly achieved by analyzing chemical maps generated from hyperspectral imaging datasets, particularly scanning electron microscope - energy dispersive X-ray spectroscopy (SEM-EDS). However, the accuracy and reliability of mineral identification are often limited by subjective human interpretation, non- ideal sample preparation, and the presence of mixed chemical signals generated within the electron-beam interaction volume. Machine learning has emerged as a powerful tool to overcome these problems. Here, we propose a machine-learning approach to identify unknown phases and unmix their overlapped chemical signals. This approach leverages the guidance of Gaussian mixture modeling clustering fitted on an informative latent space of pixel-wise elemental datapoints modeled using a neural network autoencoder, and unmixes the overlapped chemical signals of phases using non-negative matrix factorization. We evaluate the reliability and the accuracy of the new approach using two SEM-EDS datasets: a synthetic mixture sample and a real-world particulate matter sample. In the former, the proposed approach successfully identifies all major phases and extracts background-subtracted single-phase chemical signals. The unmixed chemical spectra show an average similarity of 83.0% with the ground truth spectra. In the second case, the approach demonstrates the ability to identify potentially magnetic Fe-bearing particles and their background-subtracted chemical signals. We demonstrate a flexible and adaptable approach that brings a significant improvement to mineralogical and chemical analysis in a fully automated manner. The proposed analysis process has been built into a user-friendly Python code with a graphical user interface for ease of use by general users.European Union’s Horizon 2020 research and innovation programme under grant agreement No 101005611. Electron and X-ray microscopy Community for structural and chemical Imaging Techniques for Earth materials (EXCITE) (award number - G106564). Swiss National Science Foundation (SNSF) postdoctoral mobility 672 fellowships P2ELP2_184386

Non-negative matrix factorization-aided phase unmixing and trace element quantification of STEM-EDXS data

International audienc

Carbonate stability in the reduced lower mantle

International audienceCarbonate minerals are important hosts of carbon in the crust and mantle with a key role in the transport and storage of carbon in Earth's deep interior over the history of the planet. Whether subducted carbonates efficiently melt and break down due to interactions with reduced phases or are preserved to great depths and ultimately reach the core-mantle boundary remains controversial. In this study, experiments in the laser-heated diamond anvil cell (LHDAC) on layered samples of dolomite (Mg,Ca)CO3 and iron at pressure and temperature conditions 23 reaching those of the deep lower mantle show that carbon-iron redox interactions destabilize the 24 MgCO3 component, producing a mixture of diamond, Fe7C3, and (Mg,Fe)O. However, CaCO3 is preserved, supporting its relative stability in carbonate-rich lithologies under reducing lower mantle conditions. These results constrain the thermodynamic stability of redox-driven breakdown of carbonates and demonstrate progress towards multiphase mantle petrology in the LHDAC at conditions of the lowermost mantle