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QUBIC II: Spectral polarimetry with bolometric interferometry

Bolometric interferometry is a novel technique that has the ability to perform spectral imaging. A bolometric interferometer observes the sky in a wide frequency band and can reconstruct sky maps in several sub-bands within the physical band in post-processing of the data. This provides a powerful spectral method to discriminate between the cosmic microwave background (CMB) and astrophysical foregrounds. In this paper, the methodology is illustrated with examples based on the Q & U Bolometric Interferometer for Cosmology (QUBIC) which is a ground-based instrument designed to measure the B-mode polarization of the sky at millimeter wavelengths. We consider the specific cases of point source reconstruction and Galactic dust mapping and we characterize the point spread function as a function of frequency. We study the noise properties of spectral imaging, especially the correlations between sub-bands, using end-to-end simulations together with a fast noise simulator. Finally, we conclude showing that spectral imaging performance are nearly optimal up to five sub-bands in the case of QUBIC.

79 ASTRONOMY AND ASTROPHYSICS↗

Molecular Reaction Imaging of a Surface Recombination Process Explains Performance Variation Among Smooth MoS 2 Photoelectrodes

Transition metal dichalcogenides (TMD) such as WSe 2 and MoS 2 are highly efficient and stable light absorbers in TMD∣I − ,I 3 − ∣Pt liquid junction solar cells. It is generally accepted that TMD crystals with a large fraction of exposed edge sites exhibit lower power conversion efficiencies (PCEs) than apparently smooth crystals. However, one open question is why does the PCE vary significantly from one crystal to another? Answering this critical question could lead to robust syntheses for high quality and uniform TMD samples. In this work, we apply nanoscale photoelectrochemical microscopy techniques to study n-type TMD nanoflake∣I − ,I 3 − ∣Pt cells. Using a combination of near-diffraction-limited photocurrent mapping and molecular reaction imaging techniques, we reveal a previously hidden surface recombination process: photogenerated holes in hidden p-type domains travel micron-scale distances parallel to the solid/liquid interface and preferentially react with iodide at step-edges. The overall efficiency of the nanoflake, as evidenced from whole nanoflake-level photoelectrochemical measurements, is dictated by the size, efficiency, and location of n- and p-type domains. Furthermore, these results provide a unifying view of efficiency losses in smooth TMD photoelectrodes and open the possibility to design electrode architectures that leverage the long-range lateral charge transport property for photoelectrocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using high spatial resolution satellite imagery to map forest burn severity across spatial scales in a Pine Barrens ecosystem

As a primary disturbance agent, fire significantly influences local processes and services of forest ecosystems. Although a variety of remote sensing based approaches have been developed and applied to Landsat mission imagery to infer burn severity at 30 m spatial resolution, forest burn severity have still been seldom assessed at fine spatial scales (≤ 5 m) from very-high-resolution (VHR) data. Here we assessed a 432 ha forest fire that occurred in April 2012 on Long Island, New York, within the Pine Barrens region, a unique but imperiled fire-dependent ecosystem in the northeastern United States. The mapping of forest burn severity was explored here at fine spatial scales, for the first time using remotely sensed spectral indices and a set of Multiple Endmember Spectral Mixture Analysis (MESMA) fraction images from bi-temporal — pre- and post-fire event — WorldView-2 (WV-2) imagery at 2 m spatial resolution. We first evaluated our approach using 1 m by 1 m validation points at the sub-crown scale per severity class (i.e. unburned, low, moderate, and high severity) from the post-fire 0.10 m color aerial ortho-photos; then, we validated the burn severity mapping of geo-referenced dominant tree crowns (crown scale) and 15 m by 15 m fixed-area plots (inter-crown scale) with the post-fire 0.10 m aerial ortho-photos and measured crown information of twenty forest inventory plots. Our approach can accurately assess forest burn severity at the sub-crown (overall accuracy is 84% with a Kappa value of 0.77), crown (overall accuracy is 82% with a Kappa value of 0.76), and inter-crown scales (89% of the variation in estimated burn severity ratings (i.e. Geo-Composite Burn Index (CBI)). Lastly, this work highlights that forest burn severity mapping from VHR data can capture heterogeneous fire patterns at fine spatial scales over the large spatial extents. This is important since most ecological processes associated with fire effects vary at the < 30 m scale and VHR approaches could significantly advance our ability to characterize fire effects on forest ecosystems.

54 ENVIRONMENTAL SCIENCES↗

Note: A simple method to suppress the artificial noise for velocity map imaging spectroscopy

A simple method has been proposed to suppress artificial noise from the counts with respect to the central line (or point) for the reconstructed 3D images with cylindrical symmetry in the velocity-map imaging spectroscopy. A raw 2D projection around the z-axis (usually referred to as central line) for photodetachment, photoionization, or photodissociation experiments is pre-processed via angular tailored method to avoid the signal counts distributed near the central line (or point). Two types of photoelectron velocity-map imaging (O{sup −} and Au{sup −} ⋅ NH{sub 3}) are demonstrated to give rise to the 3D images with significantly reduced central line noise after pre-processing operation. The major advantages of the pre-operation are the ability of suppression of central-line noise to resolve weak structures or vibrational excitation in atoms or molecules near photon threshold.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Quasi-Steady-State Polarization Reveals the Interplay of Capacitive and Faradaic Processes in Capacitive Deionization

We employ slow cyclic voltammetry to study the quasi-steady-state capacitive deionization (CDI) of aerated 10 mM NaCl from V cell =-0.2 to 2 V. The method allows for the deconvolution of capacitive and faradaic processes, which are significant even at low voltage, in conjunction with pH, conductivity, dissolved oxygen (DO), and electrode potential measurements. The pH at three locations and effluent DO data identify asymmetric electrosorption in the cell configured with pristine activated carbon electrodes, where charge is irreversibly consumed to produce H + /OH - instead of reversibly adsorbing Cl - /Na + . Implementing a reference electrode resolves ion adsorption as a function of the individual potential at each electrode. Near-electrode pH probes reveal pH environments that diverge by up to 8 units during cell polarization and allow more accurate calculation of faradaic redox potentials in a flow-by CDI cell. In the aerated NaCl solution that will be relevant to industrial-scale water treatment, we find that DO reduction occurs to a greater degree than Na + adsorption at the cathode until DO removal becomes mass transfer limited at <-0.2 V vs. SHE. Two cell architectures – flow-by and flow-through – corroborate our findings. Finally, we reconcile all measurements to generate a map displaying how the potential is partitioned amongst the capacitive and faradaic processes occurring during CDI operation over a 2.2 V window.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Estimating snow cover from high-resolution satellite imagery by thresholding blue wavelengths

We report the extent and duration of snow cover, a critical component of the hydrologic cycle and the global climate system, is expected to shift dramatically under climate change. Therefore, developing high-resolution assessments of snow cover change is crucial for estimating the impact of changing snow cover on watershed and ecosystems processes in cold regions. Remote sensing tools provide a powerful method for mapping snow-covered area (SCA) across a landscape. The most common method for estimating SCA utilizes the normalized difference snow index (NDSI), which relies on spectral measurements in the shortwave-infrared wavelengths (SWIR). NDSI can effectively estimate catchment- to regional-scale SCA, but it cannot be used to assess fine-scale SCA because of current limitations on the spatial resolution of satellite-derived SWIR measurements. Here, we map SCA using a threshold of blue wavelengths and high-resolution satellite imagery. The thresholding method, which we call the Blue Snow Threshold algorithm (BST), has previously been used with digital camera imagery. We refine and automate the algorithm for use with cloud-free high-resolution satellite imagery and find that the BST can be used to assess fine-scale SCA. For validation, we compared BST-derived estimates of SCA to a) airborne lidar surveys, b) Landsat fractional SCA, and c) snow disappearance dates from Snow Telemetry (SNOTEL) stations. When compared to airborne lidar surveys of SCA, the BST predicted SCA had a range of F-scores between 0.81 and 0.94 in four study areas in California and Colorado. We also found general agreement between SCA and snow disappearance at multiple SNOTEL sites across the western United States. Given the relatively recent availability of high-resolution satellite imagery with spectral measurements in the visible wavelengths but lacking in SWIR, the BST offers a reliable and easy-to-apply tool for examining fine-scale snow-related processes.

54 ENVIRONMENTAL SCIENCES↗

Utilization of GIS technology to support development of flow and contaminant fate and transport models at US DOE sites - 15457

U.S. Department of Energy (DOE) sites have accumulated years of data and millions of spatial and temporal records related to the hydrological cycle, contaminant transport, and parameters of remediation technologies. In addition, numerical models which use field monitoring data to help understand flow and transport produce gigabytes of computed spatial and temporal data for each computation node. There is a need therefore for an advanced spatial data structure that can be used to address the management, processing, and analysis of spatial and temporal numerical modeling data derived from multiple sources. This can be accomplished using a geo-database. The development of an ArcSDE geo-database facilitates the centralized storage, backup, accessibility, organization, and management of model configuration and computed simulation data, putting it into a structured, coherent, and logical computer-supported system. GIS data processing and automation would enable faster and hence more complex analyses of field test data. The Applied Research Center (ARC) at Florida International University (FIU) has provided analysis of flow and transport for several watersheds at DOE's Oak Ridge Reservation (ORR), including East Fork Poplar Creek (EFPC), Upper EFPC in the Y-12 National Security Complex area (Y-12 NSC) and White Oak Creek (WOC). Integrated surface and subsurface flow, fate and transport models were developed to provide analysis of contaminant patterns within each watershed. In addition, digital monitoring data available from the Oak Ridge Environmental Information System (OREIS) related to mercury (Hg) contamination and remediation within these watersheds was used for calibration and verification of the model. Experimental studies were also carried out which provided kinetic and equilibrium data about important parameters related to Hg transport, speciation and methylation/demethylation kinetics within the watershed. Geographic Information Systems (GIS) technology was employed to support the modeling work through storage and geo-processing of spatial and temporal data required by the models and to produce hydrogeological maps for visualization. An ArcGIS geo-database was developed for centralized storage and management of experimental and computed model data and its capabilities were extended over the years using tools such as ModelBuilder combined with Python scripting to automate repetitive tasks, perform statistical analyses and generate maps and reports. The hydrologic geo-database model developed possesses a structure that enables linkage with scalable hydrologic modeling tools/applications to model hydrologic systems, and in this case, enables the testing of the potential impacts of various remediation scenarios on the ORR watersheds. The ArcSDE geo-database can also be used to automate and simplify the process of calling stored GIS and time series data. This geo-database can serve as a tool for contaminant flow and transport analyses which require large amounts of high-quality spatial and temporal data in order to ensure reliability and validity of modeling results. The existing geo-database structure developed for the hydrological modeling at ORR was designed to be replicable for application at other DOE sites. An investigation of downloadable free/open source GIS software along with required security protocols to facilitate online querying of the database was also conducted to determine methods by which project-derived data can be more easily shared with other project stakeholders such as DOE personnel and site contractors. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Emerging Technologies and Techniques for Wide Area Radiological Survey and Remediation

Technologies to survey and decontaminate wide-area contamination and process the subsequent radioactive waste have been developed and implemented following the Chernobyl nuclear power plant release and the breach of a radiological source resulting in contamination in Goiania, Brazil. These civilian examples of radioactive material releases provided some of the first examples of urban radiological remediation. Many emerging technologies have recently been developed and demonstrated in Japan following the release of radioactive cesium isotopes (Cs-134 and Cs-137) from the Fukushima Dai-ichi nuclear power plant in 2011. Information on technologies reported by several Japanese government agencies, such as the Japan Atomic Energy Agency (JAEA), the Ministry of the Environment (MOE) and the National Institute for Environmental Science (NIES), together with academic institutions and industry are summarized and compared to recently developed, deployed and available technologies in the United States. The technologies and techniques presented in this report may be deployed in response to a wide area contamination event in the United States. In some cases, additional research and testing is needed to adequately validate the technology effectiveness over wide areas. Survey techniques can be deployed on the ground or from the air, allowing a range of coverage rates and sensitivities. Survey technologies also include those useful in measuring decontamination progress and mapping contamination. Decontamination technologies and techniques range from non-destructive (e.g., high pressure washing) and minimally destructive (plowing), to fully destructive (surface removal or demolition). Waste minimization techniques can greatly impact the long-term environmental consequences and cost following remediation efforts. Recommendations on technical improvements to address technology gaps are presented together with observations on remediation in Japan.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

An Automated Method for Mapping Giant Kelp Canopy Dynamics from UAV

Satellite and aerial imagery have been used extensively for mapping the abundance and distribution of giant kelp ( Macrocystis pyrifera ) in southern California. There is now great potential for using unoccupied aerial vehicles (UAVs) to map kelp canopy at very high resolutions. However, tides and currents have been shown to affect the amount of floating kelp canopy on the water surface, and the impacts of these processes on remotely sensed kelp estimates in this region have not been fully quantified. UAVs were used to map fine-scale changes in canopy area due to tidal height and current speed at kelp forests off the coast of Palos Verdes, CA and Santa Barbara, CA. An automated method for detecting kelp canopy was developed that was 67% accurate using red-green-blue (RGB) UAV imagery and 93% accurate using multispectral UAV imagery across a range of weather, ocean, and illumination conditions. Increases in tidal height of 1 m reduced the amount of floating kelp canopy by 15% in Santa Barbara and by over 30% in Palos Verdes. The effect of current speed on visible kelp canopy was inconclusive, but there was a trend towards lower canopy area with increased current speed. Therefore, while tidal height and current speed can introduce significant variability to estimates of kelp abundance, the magnitude of this variability is site specific. Still, UAVs are a valuable tool for mapping of kelp canopy and can provide greater spatial resolution and temporal coverage than is possible from many satellite sensors. This data can provide insight into the patterns and drivers of high frequency fluctuations in kelp abundance.

54 ENVIRONMENTAL SCIENCES↗

Changes in soil pore structure generated by the root systems of maize , sorghum and switchgrass affect in situ N 2 O emissions and bacterial denitrification

Due to the heterogeneous nature of soil pore structure, processes such as nitrification and denitrification can occur simultaneously at microscopic levels, making prediction of small-scale nitrous oxide (N 2 O) emissions in the field notoriously difficult. We assessed N 2 O+N 2 emissions from soils under maize (Zea mays L.), switchgrass (Panicum virgatum L.), and energy sorghum (Sorghum bicolor L.), three potential bioenergy crops in order to identify the importance of different N 2 O sources to microsite production, and relate N 2 O source differences to crop-associated differences in pore structure formation. The combination of isotopic surveys of N 2 O in the field during one growing season and X-ray computed tomography (CT) enabled us to link results from isotopic mappings to soil structural properties. Further, our methodology allowed us to evaluate the potential for in situ N 2 O suppression by biological nitrification inhibition (BNI) in energy sorghum. Our results demonstrated that the fraction of N 2 O originating from bacterial denitrification and reduction of N 2 O to N 2 is largely determined by the volume of particulate organic matter occluded within the soil matrix and the anaerobic soil volume. Bacterial denitrification was greater in switchgrass than in the annual crops, related to changes in pore structure caused by the coarse root system. This led to high N-loses through N 2 emissions in the switchgrass system throughout the season a novel finding given the lack of data in the literature for total denitrification. Isotopic mapping indicated no differences in N 2 O-fluxes or their source processes between maize and energy sorghum that could be associated with the release of BNI by the investigated sorghum variety. The results of this research show how differences in soil pore structures among cropping systems can determine both N 2 O production via denitrification and total denitrification N losses in situ.

59 BASIC BIOLOGICAL SCIENCES↗

Energy landscapes from cryo-EM snapshots: a benchmarking study

Abstract Biomolecules undergo continuous conformational motions, a subset of which are functionally relevant. Understanding, and ultimately controlling biomolecular function are predicated on the ability to map continuous conformational motions, and identify the functionally relevant conformational trajectories. For equilibrium and near-equilibrium processes, function proceeds along minimum-energy pathways on one or more energy landscapes, because higher-energy conformations are only weakly occupied. With the growing interest in identifying functional trajectories, the need for reliable mapping of energy landscapes has become paramount. In response, various data-analytical tools for determining structural variability are emerging. A key question concerns the veracity with which each data-analytical tool can extract functionally relevant conformational trajectories from a collection of single-particle cryo-EM snapshots. Using synthetic data as an independently known ground truth, we benchmark the ability of four leading algorithms to determine biomolecular energy landscapes and identify the functionally relevant conformational paths on these landscapes. Such benchmarking is essential for systematic progress toward atomic-level movies of continuous biomolecular function.

59 BASIC BIOLOGICAL SCIENCES↗

Accurate and efficient prediction of fine-resolution hydrologic and carbon dynamic simulations from coarse-resolution models

The topography, and the biotic and abiotic parameters are typically upscaled to make watershed-scale hydrologic-biogeochemical models computationally tractable. However, upscaling procedure can produce biases when nonlinear interactions between different processes are not fully captured at coarse resolutions. Here, we applied the Proper Orthogonal Decomposition Mapping Method (PODMM) to downscale the field solutions from a coarse (7 km) resolution grid to a fine (220 m) resolution grid. PODMM trains a reduced-order model (ROM) with coarse-resolution and fine-resolution solutions, here obtained using PAWS+CLM, a quasi-3-D watershed processes model that has been validated for many temperate watersheds. Subsequent fine-resolution solutions were approximated based only on coarse-resolution solutions and the ROM. The approximation errors were efficiently quantified using an error estimator. By jointly estimating correlated variables and temporally varying the ROM parameters, we further reduced the approximation errors by up to 20%. We also improved the method's robustness by constructing multiple ROMs using different set of variables, and selecting the best approximation based on the error estimator. The ROMs produced accurate downscaling of soil moisture, latent heat flux, and net primary production with O(1000) reduction in computational cost. The subgrid distributions were also nearly indistinguishable from the ones obtained using the fine-resolution model. Compared to coarse-resolution solutions, biases in upscaled ROM solutions were reduced by up to 80%. This method has the potential to help address the long-standing spatial scaling problem in hydrology and enable long-time integration, parameter estimation, and stochastic uncertainty analysis while accurately representing the heterogeneities.

58 GEOSCIENCES↗

Physics-informed KNN milling stability model with process damping effects

This paper describes a k-nearest neighbors, or KNN, model for milling stability including process damping effects. A physics-based, frequency domain milling stability solution is used to generate the training data, but does not incorporate process damping effects. The data set is then updated using limited tests to capture the process damping behavior. A “stair step” approach is used to select the test points, where a first spindle speed-axial depth combination is selected based on the physics-based stability map, subsequent tests are defined using the previous test result, and data points are updated by knowledge of process damping behavior and the test results. Furthermore, the KNN modeling approach demonstrates the ability to predict both stable and unstable results, including process damping behavior.

42 ENGINEERING↗

Searching for the origin of the rare-earth peak with precision mass measurements across Ce–Eu isotopic chains

A nuclear mass survey of rare-earth isotopes has been conducted with the Canadian Penning Trap mass spectrometer using the most neutron-rich nuclei thus far extracted from the CARIBU facility. Here, we present a collection of 12 nuclear masses determined with a precision of ≤ 10 keV/c 2 for Z = 58-63 nuclei near N = 100. Independently, a detailed study exploring the role of nuclear masses in the formation of the r-process rare-earth abundance peak has been performed. Employing a Markov chain Monte Carlo (MCMC) technique, mass predictions of lanthanide isotopes have been made which uniquely reproduce the observed solar abundances near A = 164 under three distinct astrophysical outflow conditions. We demonstrate that the mass surface trends thus far mapped out by our measurements are most consistent with MCMC mass predictions given an r process that forms the rare-earth peak during an extended (n, γ) ⇌ (γ, n) equilibrium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mapped Moments to a Cartesian Grid (MMCG) Value-Added Product Report

Objective analysis (OA) is a method of mapping unstructured data to a structured grid. In the context of scanning radar data, OA is used to interpolate data in antenna coordinates (range, azimuth, and elevation) onto a regularly spaced Cartesian grid (Trapp and Doswell 2000). The U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility’s Mapped Moments to a Cartesian Grid (MMCG) Value-Added Product (VAP) uses the Python ARM Radar Toolkit (Py-ART), a data model-driven interactive architecture for working with weather radar data, to map the data to a Cartesian grid (Helmus and Collis 2016). MMCG, with Py-ART built in, has the ability to take radar data in antenna coordinates and map the gates to a Cartesian grid using inverse distance weight functions such as Cressman (square) and Barnes (exponential), but also can filter the data during the interpolation. MMCG also allows arbitrary formulations for the radius of influence, which are matched to particular radar scanning strategies. This creates a complex parameter space for optimizing the retention of storm structure detail while minimizing artifacts. MMCG takes data processed with ARM’s Corrected Precipitation Radar Moments in Antenna Coordinates (CMAC) VAP and maps it to a Cartesian grid as the output product. A variety of fields that have been mapped to the Cartesian grid are then saved to plots to complement each grid file.

54 ENVIRONMENTAL SCIENCES↗

In situ Detection of Plasma Induced Surface Interaction based on Deep Learning based Visual Diagnostics (Technical Report)

It is characteristic for many plasma devices to undergo plasma-material interaction leading to surface erosion. These processes, often not easily detectable, lead to changes in device performance and lifespan. State-of-the-art lifetime tests and wear experiments require over 1000s hours. A self-consistent model for accurately predicting the erosion's effects is not available. In situ detection of these processes is not a trivial task since the surface variations at the early stages have a micron scale. Such limitations not only restrict testing and prediction capabilities but also slow the development of new thrusters and limit mission duration. To address these challenges, an in-situ diagnostic for real-time erosion assessment has been developed, aiming to expedite lifetime testing and broaden experimental campaigns. Several works were dedicated to real-time and in situ monitoring of material erosion during plasma exposure using laser holography, microscopy, and with telemicroscopes. However, the applicability of these approaches is limited due to complexity, cost and less flexibility as they often require placing diagnostic equipment inside the vacuum chamber. In collaboration with Princeton Collaborative Research Facility (PCRF), Princeton Plasma Physics Laboratory (PPPL), a new diagnostic approach is developed, where geometry modifications to the ceramic channel walls were introduced that would result in accelerated channel erosion. We employed Long-distance microscope (LDM) imagery, combined with Deep-Learning based Shape from focus or depth from focus (DFF or SFF) approach, that provides an accessible and cost-effective solution. LDM employs focus variation techniques to continuously capture multiple images of the target object at distinct focal planes. DFF, an optical focus variation method, generates a 3D topographical surface depth map from a sequence of variably focused images. Combined with the developed diagnostic, this approach offers a controllable means to study erosion under accelerated conditions. In this work, we develop Neural Network-based DFF algorithm applicable for LDM data to quantitatively evaluate plasma induced surface modification from LDM data. Next, we develop Deep Learning-based super-resolution depth map image reconstruction technique to increase the resolution of depth maps obtained from DFF algorithm to improve the accuracy of erosion measurements. Thirdly, we develop several image processing techniques to remove noise and improve the quality of depth map image. Here we report the results of initial tests for this approach. An experimental setup designed and built in PPPL was employed that consists of a 3-cm gridded ion source that produces a neutralized argon beam with energies up to 600 eV. A hexagonal boron nitride (h-BN) ceramic target, designed based on computational predictions, was used. Tests were conducted to reconstruct the complex geometry of the target under the lighting conditions of the operated ion source.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Advances in bone preservation: Identifying possible collagen preservation using sulfur speciation mapping

The complexity and heterogeneity of bone chemistry makes it difficult to discern information on physiological and taphonomic processes stored within the bone matrix. Analysis of archaeological and palaeontological bone becomes more difficult because in many cases the most pivotal specimens are too scientifically valuable for destructive analysis. Here, this problem is further escalated by the fact that the heterogeneity of the bone may cause small “pockets” of preservation that can be missed during sampling. Therefore, a non-destructive technique that can spatially resolve such heterogeneity within the bone is needed.

36 MATERIALS SCIENCE↗

Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce “Blackout Diffusion”, which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Santos, Javier E.↗