Discrete Diffusion Models Research Articles

Discrete diffusion models with Refined Language-Image Pre-trained representations for remote sensing image captioning

RS image captioning (RSIC) utilizes natural language to provide a description of image content, assisting in the comprehension of object properties and relationships. Nonetheless, RS images are characterized by variations in object scales, distributions, and quantities, which make it challenging to obtain global semantic information and object connections. To enhance the accuracy of captions produced from RS images, this paper proposes a novel method referred to as Discrete Diffusion Models with Refined Language-Image Pre-trained representations (DDM-RLIP), leveraging an advanced discrete diffusion model (DDM) for nosing and denoising text tokens. DDM-RLIP is based on an advanced DDM-based method designed for natural pictures. The primary approach for refining image representations involves fine-tuning a CLIP image encoder on RS images, followed by adapting the transformer with an additional attention module to focus on crucial image regions and relevant words. Furthermore, experiments were conducted on three datasets, Sydney-Captions, UCM-Captions, and NWPU-Captions, and the results demonstrated the superior performance of the proposed method compared to conventional autoregressive models. On the NWPU-Captions dataset, the CIDEr score improved from 116.4 to 197.7, further validating the efficacy and potential of DDM-RLIP. The implementation codes for our approach DDM-RLIP are available at https://github.com/Leng-bingo/DDM-RLIP.

SchröWave: Realistic voice generation by solving two-stage conditional Schrödinger bridge problems

In recent years, methods based on discrete diffusion models have achieved state-of-the-art performances in voice generation [1,2]. In theory, the voice data can be transformed into the exact Gaussian prior distributions only when the diffusion time tends to infinity. But in real applications, the Gaussian prior distribution can only be achieved approximately in a limited time duration run by these diffusion-based methods, thus resulting in sub-optimal sound quality. In this paper, we present the SchröWave to realize the continuous transformation from exact Dirac's deltas to the target voice data distribution in finite time duration, conditioned on middle voice representation with different sizes. At the same time, in order to overcome the difficulty in calculating the score on the low-dimensional manifold of voice data during the generation process, we propose to use a two-stage diffusion and generation method, while each stage implemented by solving a conditional Schrödinger bridge problem. Our experiments on the public data set LJSpeech show that the effect is significant in both objective and subjective evaluation, and achieve the new state-of-the-art MOS of 4.53. Audio samples are available at https://schrowave.github.io.

Linking discrete and continuum diffusion models: Well‐posedness and stable finite element discretizations

AbstractIn the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well‐understood, particularly in relation to the well‐posedness of the ensemble. In this article, we focus on combining two classes of dissimilar diffusive models: the first one defined over a continuum and the second one based on discrete equations that connect average values of the solution over disjoint subdomains. For stationary problems, we show unconditional stability of the linked problems and then the stability and convergence of its discretized counterpart when mixed finite elements are used to approximate the model on the continuum. The theoretical results are highlighted with numerical examples illustrating the effects of linking diffusive models. As a side result, we show that the methods introduced in this article can be used to infer the solution of diffusive problems with incomplete data.

Homogenization of discrete diffusion models by asymptotic expansion

AbstractDiffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This burden can be partially decreased by using discrete models, however even then the practical application is limited to relatively small material volumes. This paper formulates a homogenization scheme for discrete diffusion models. Asymptotic expansion homogenization is applied to distinguish between (i) the continuous macroscale description approximated by the standard finite element method and (ii) the fully resolved discrete mesoscale description in a local representative volume element (RVE) of material. Both transient and steady‐state variants with nonlinear constitutive relations are discussed. In all the cases, the resulting discrete RVE problem becomes a simple linear steady‐state problem that can be easily pre‐computed. The scale separation provides a significant reduction of computational time allowing the solution of practical problems with a negligible error introduced mainly by the finite element discretization at the macroscale.

Phylodynamic Dispersal of SARS-CoV-2 Lineages Circulating across Polish-German Border Provinces.

Introduction: The emergence of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has evolved into a worldwide outbreak, with significant molecular evolution over time. Large-scale phylodynamic studies allow to map the virus spread and inform preventive strategies. Aim: This study investigates the extent of binational dispersal and dynamics of SARS-CoV-2 lineages between seven border provinces of the adjacent countries of Poland and Germany to reconstruct SARS-CoV-2 transmission networks. Methods: Following three pandemic waves from March 2020 to the end of May 2021, we analysed a dataset of 19,994 sequences divided into B.1.1.7|Alpha and non-Alpha lineage groups. We performed phylogeographic analyses using the discrete diffusion models to identify the pathways of virus spread. Results: Based on population dynamics inferences, in total, 673 lineage introductions (95% HPD interval 641–712) for non-Alpha and 618 (95% HPD interval 599–639) for B.1.1.7|Alpha were identified in the area. For non-Alpha lineages, 5.05% binational, 86.63% exclusively German, and 8.32% Polish clusters were found, with a higher frequency of international clustering observed for B.1.1.7|Alpha (13.11% for binational, 68.44% German and 18.45% Polish, p < 0.001). We identified key transmission hubs for the analysed lineages, namely Saxony, West Pomerania and Lower Silesia. Conclusions: Clustering patterns between Poland and Germany reflect the viral variant transmission dynamics at the international level in the borderline area. Tracing the spread of the virus between two adjacent large European countries may provide a basis for future intervention policies in cross-border cooperation efforts against the spread of the pandemics.

Agricultural and geographic factors shaped the North American 2015 highly pathogenic avian influenza H5N2 outbreak.

The 2014–2015 highly pathogenic avian influenza (HPAI) H5NX outbreak represents the largest and most expensive HPAI outbreak in the United States to date. Despite extensive traditional and molecular epidemiological studies, factors associated with the spread of HPAI among midwestern poultry premises remain unclear. To better understand the dynamics of this outbreak, 182 full genome HPAI H5N2 sequences isolated from commercial layer chicken and turkey production premises were analyzed using evolutionary models able to accommodate epidemiological and geographic information. Epidemiological compartmental models embedded in a phylogenetic framework provided evidence that poultry type acted as a barrier to the transmission of virus among midwestern poultry farms. Furthermore, after initial introduction, the propagation of HPAI cases was self-sustainable within the commercial poultry industries. Discrete trait diffusion models indicated that within state viral transitions occurred more frequently than inter-state transitions. Distance and sample size were very strongly supported as associated with viral transition between county groups (Bayes Factor > 30.0). Together these findings indicate that the different types of midwestern poultry industries were not a single homogenous population, but rather, the outbreak was shaped by poultry industries and geographic factors.

Time-scaled phylogeography of complete Zika virus genomes using discrete and continuous space diffusion models

Zika virus (ZIKV), a vector-borne infectious agent that has recently been associated with neurological diseases and congenital microcephaly, was first reported in the Western hemisphere in early 2015.A number of authors have reconstructed its epidemiological history using advanced phylogenetic approaches, and the majority of Zika phylogeography studies have used discrete diffusion models. Continuous space diffusion models make it possible to infer the possible origin of the virus in real space by reconstructing its ancestral location on the basis of geographical coordinates deduced from the latitude and longitude of the sampling locations. We analysed all the ZIKV complete genome isolates whose sampling times and localities were available in public databases at the time the study began, using a Bayesian approach for discrete and continuous phylogeographic reconstruction.The discrete phylogeographic analysis suggested that ZIKV emerged to become endemic/epidemic in the first decade of the 1900s in the Ugandan rainforests, and then reached Western Africa and Asia between the 1930s and 1950s. After a long period of about 40 years, it spread to the Pacific islands and reached Brazil from French Polynesia. Continuous phylogeography of the American epidemic showed that the virus entered in north-eastern Brazil in late 2012 and started to spread in early 2013 from two high probability regions: one corresponding to the entire north-east Brazil and the second surrounding the city of Rio de Janeiro, in a mainly northwesterly direction to Central America, the north-western countries of south America and the Caribbean islands. Our data suggest its cryptic circulation in both French Polynesia and Brazil, thus raising questions about the mechanisms underlying its undetected persistence in the absence of a known animal reservoir, and underline the importance of continuous diffusion models in making more reliable phylogeographic reconstructions of emerging viruses.

Evolution of dispersal in a spatially periodic integrodifference model

An integrodifference model describing the reproduction and dispersal of a population is introduced to investigate the evolution of dispersal in a spatially periodic habitat. The dispersal is determined by a kernel function, and the dispersal strategy is defined as the probability of population individuals’ moving to a different habitat. Both conditional and unconditional dispersal strategies are investigated, the distinction being whether dispersal depends on local environmental conditions. For competing unconditional dispersers, we prove that the population with the smaller dispersal probability always prevails. Alternatively, for conditional dispersers, it is shown that the strategy known as ideal free dispersal is both sufficient and necessary for evolutionary stability. These results extend those in the literature for discrete diffusion models in finite patchy landscapes and from reaction–diffusion models.

Multiple Cross-Species Transmission Events of Human Adenoviruses (HAdV) during Hominine Evolution.

Human adenoviruses (HAdV; species HAdV-A to -G) are highly prevalent in the human population, and represent an important cause of morbidity and, to a lesser extent, mortality. Recent studies have identified close relatives of these viruses in African great apes, suggesting that some HAdV may be of zoonotic origin. We analyzed more than 800 fecal samples from wild African great apes and humans to further investigate the evolutionary history and zoonotic potential of hominine HAdV. HAdV-B and -E were frequently detected in wild gorillas (55%) and chimpanzees (25%), respectively. Bayesian ancestral host reconstruction under discrete diffusion models supported a gorilla and chimpanzee origin for these viral species. Host switches were relatively rare along HAdV evolution, with about ten events recorded in 4.5 My. Despite presumably rare direct contact between sympatric populations of the two species, transmission events from gorillas to chimpanzees were observed, suggesting that habitat and dietary overlap may lead to fecal-oral cross-hominine transmission of HAdV. Finally, we determined that two independent HAdV-B transmission events to humans occurred more than 100,000 years ago. We conclude that HAdV-B circulating in humans are of zoonotic origin and have probably affected global human health for most of our species lifetime.

Phylogeographic Reconstruction of African Yellow Fever Virus Isolates Indicates Recent Simultaneous Dispersal into East and West Africa

Yellow fever virus (YFV) is a mosquito-borne flavivirus that is a major public health problem in tropical areas of Africa and South America. There have been detailed studies on YFV ecology in West Africa and South America, but current understanding of YFV circulation on the African continent is incomplete. This inadequacy is especially notable for East and Central Africa, for which the unpredictability of human outbreaks is compounded by limitations in both historical and present surveillance efforts. Sparse availability of nucleotide sequence data makes it difficult to investigate the dispersal of YFV in these regions of the continent. To remedy this, we constructed Bayesian phylogenetic and geographic analyses utilizing 49 partial genomic sequences to infer the structure of YFV divergence across the known range of the virus on the African continent. Relaxed clock analysis demonstrated evidence for simultaneous divergence of YFV into east and west lineages, a finding that differs from previous hypotheses of YFV dispersal from reservoirs located on edges of the endemic range. Using discrete and continuous geographic diffusion models, we provide detailed structure of YFV lineage diversity. Significant transition links between extant East and West African lineages are presented, implying connection between areas of known sylvatic cycling. The results of demographic modeling reinforce the existence of a stably maintained population of YFV with spillover events into human populations occurring periodically. Geographically distinct foci of circulation are reconstructed, which have significant implications for studies of YFV ecology and emergence of human disease. We propose further incorporation of Bayesian phylogeography into formal GIS analyses to augment studies of arboviral disease.

The implications of model formulation when transitioning from spatial to landscape ecology

In this article we compare and contrast the predictions of some spatially explicit and implicit models in the context of a thought problem at the interface of spatial and landscape ecology. The situation we envision is a one-dimensional spatial universe of infinite extent in which there are two disjoint focal patches of a habitat type that is favorable to some specified species. We assume that neither patch is large enough by itself to sustain the species in question indefinitely, but that a single patch of size equal to the combined sizes of the two focal patches provides enough contiguous favorable habitat to sustain the given species indefinitely. When the two patches are separated by a patch of unfavorable matrix habitat, the natural expectation is that the species should persist indefinitely if the two patches are close enough to each other but should go extinct over time when the patches are far enough apart. Our focus here is to examine how different mathematical regimes may be employed to model this situation, with an eye toward exploring the trade-off between the mathematical tractability of the model on one hand and the suitability of its predictions on the other. In particular, we are interested in seeing how precisely the predictions of mathematically rich spatially explicit regimes (reaction-diffusion models, integro-difference models) can be matched by those of ostensibly mathematically simpler spatially implicit patch approximations (discrete-diffusion models, average dispersal success matrix models).

Evolutionary stability of ideal free nonlocal dispersal

We study the evolutionary stability of nonlocal dispersal strategies that can produce ideal free population distributions, that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium. We find that the property of producing ideal free distributions is necessary and often sufficient for evolutionary stability. Our results extend those already developed for discrete diffusion models on finite patch networks to the case of nonlocal dispersal models based on integrodifferential equations. The analysis is based on the use of comparison methods and the construction of sub- and supersolutions.

Discrete diffusion models to study the effects of Mg2+ concentration on the PhoPQ signal transduction system

BackgroundThe challenge today is to develop a modeling and simulation paradigm that integrates structural, molecular and genetic data for a quantitative understanding of physiology and behavior of biological processes at multiple scales. This modeling method requires techniques that maintain a reasonable accuracy of the biological process and also reduces the computational overhead. This objective motivates the use of new methods that can transform the problem from energy and affinity based modeling to information theory based modeling. To achieve this, we transform all dynamics within the cell into a random event time, which is specified through an information domain measure like probability distribution. This allows us to use the “in silico” stochastic event based modeling approach to find the molecular dynamics of the system.ResultsIn this paper, we present the discrete event simulation concept using the example of the signal transduction cascade triggered by extra-cellular Mg2+ concentration in the two component PhoPQ regulatory system of Salmonella Typhimurium. We also present a model to compute the information domain measure of the molecular transport process by estimating the statistical parameters of inter-arrival time between molecules/ions coming to a cell receptor as external signal. This model transforms the diffusion process into the information theory measure of stochastic event completion time to get the distribution of the Mg2+ departure events. Using these molecular transport models, we next study the in-silico effects of this external trigger on the PhoPQ system.ConclusionsOur results illustrate the accuracy of the proposed diffusion models in explaining the molecular/ionic transport processes inside the cell. Also, the proposed simulation framework can incorporate the stochasticity in cellular environments to a certain degree of accuracy. We expect that this scalable simulation platform will be able to model more complex biological systems with reasonable accuracy to understand their temporal dynamics.

A markov chain approach to complex diffusion processes superimposed by adsorption or chemical reaction

On the basis of a critical analysis of previous publications (Pippel and Philipp, 1977a, Chem. Engng Sci. 32, 543–549; 1997b, Chem. Engng Sci. 32, 1535–1536) revised discrete stochastic diffusion models are presented for describing the dynamics of mass and heat transfer coupled with chemical reaction and adsorption. In particular, a more correct mathematical expression of the transition probability matrix has been derived from the concepts of stochastic process theory. The model can be used for systems with constant as well as nonconstant process coefficients by using inhomogeneous Markov chains in the latter case. The validity of the model has been tested by comparison of its results with analytical solutions. The versatility and usefulness of the model will be demonstrated by different examples.

Inverse diffusion methods for data peak separation

Previous methods for separation of overlapping data peaks include geometrical assessment and Fourier deconvolution. On the basis of inverse diffusion theory, we present new separation methods suitable for convenient programming and rapid calculation of Gaussian area contributions. Both continuum and discrete inverse diffusion models are described. Example computations are given for biological data: density gradient centrifugation, isoelectric focusing electrophoresis, and high-pressure liquid chromatography.