Everything is motion.
Ordinary and stochastic differential equations, integrated live over their own vector-field geometry. Pick a flow and watch an ensemble propagate.
Pure Mathematics · Generative Models · Stochastic Processes · Geometry & Analysis
I'm drawn, above all, to pure mathematics — and to the surprising ways it becomes the language of generative models and deep learning.
I'm drawn, above all, to pure mathematics — and to the surprising ways it becomes the language of generative models and deep learning.
My full name is Seyed MohammadHossein Hosseini Dastjae — not unlike Albus Percival Wulfric Brian Dumbledore — but I mostly go by Mamad. I hold a B.Sc. in Computer Engineering from the University of Isfahan, and I'm currently an M.Sc. student in Computer Science at the University of Padova (since October 2025), moving deliberately toward mathematics.
My centre of gravity is pure mathematics: I care most about the analytic and geometric structure beneath a model, and I find that generative modeling and deep learning are where that structure comes alive. The stochastic-calculus reading of diffusion and flow models; optimal transport as the geometry of distributions; homeomorphism interpolation by Neural ODEs; the kinship between flows and differential equations — these are the threads I keep pulling.
The directions I most want to work in are optimal transport, differential geometry, and functional analysis — and, most of all, the likely connections between stochastic differential equations, geometry, and analysis. My aim is to keep moving deeper into pure mathematics and its dialogue with generative models. If any of this overlaps with what you're thinking about, I'd be glad to hear from you.
Currently: M.Sc. Computer Science @ University of Padova · working toward pure mathematics & generative models.
I approach machine learning from pure mathematics — asking which analytic, geometric, and probabilistic structures make learning possible, and how they become concrete algorithms for generation and inference. Six threads organize the work, with optimal transport, geometry, and analysis increasingly at the centre.
The throughline: analysis, geometry, and probability as the grammar behind modern models — not decoration, but a generative source of ideas.
I believe abstract mathematics is where the good ideas in learning come from. Flows and differential equations, transport and geometry, diffusion and stochastic calculus — I want to keep pulling these threads toward a PhD in pure mathematics and generative models.
The geometry of moving one distribution onto another — Wasserstein geometry, couplings, and transport as the backbone of modern generative flows.
Optimal transport gives distributions a geometry. I'm especially interested in OT couplings that straighten generative paths — conditional flow matching with minibatch OT — and in the analytic side: Wasserstein gradient flows and their link to diffusion.
Learning to sample complex distributions — diffusion, flow matching, normalizing flows, and latent-variable models.
How do we turn noise into structure? I work across diffusion, flow matching, and exact-likelihood flows, with a bias toward the probabilistic and dynamical principles beneath the architectures.
Generation as integrating a stochastic differential equation — and the search for processes better matched to data.
The score-based view recasts generation as a reverse-time SDE. I'm interested in which stochastic processes — and which geometries on their paths — are analytically and topologically better suited to real, structured data.
Curvature, manifolds, and the shape of latent space — continuous-depth models as homeomorphisms that deform geometry.
Data and latent spaces have shape. I study manifold structure, Neural ODEs as continuous deformations preserving topology, and how curvature and geometry inform where and how models can learn.
Function spaces and operators — the analytic setting where scores, densities, and flows actually live.
Densities, score functions, and velocity fields are elements of function spaces; training is optimization over them. I want to bring the tools of analysis — operators, spaces, and their geometry — to bear on why these methods work.
A generative OT flow, stacked on a seasonal anchor, for long-horizon city traffic.
Turn noise into structure by learning to reverse a gradual diffusion.
Deterministic, few-step sampling from a diffusion model — without retraining.
Exact densities through invertible, differentiable transformations.
Fitting latent-variable models by iterated lower-bound maximization.
Measuring the shape of data across scales.
Learning how much each neighbor matters.
Extending the stochastic-differential-equation view of diffusion generative models to the structure and dependencies of time-series data.
Applying diffusion-based generative modeling to strengthen meta-learning approaches for retail demand forecasting.
A short note on why I'm reorienting my work around pure mathematics — and why generative models are where that mathematics comes alive.
ReadHow an optimal-transport coupling turns curved flow-matching trajectories into straight lines you can integrate in a handful of steps.
ReadThe best way to reach me is by email. I'm always glad to discuss generative models, stochastic processes, or potential collaborations and graduate opportunities.