PhD Position F/M Theory for Discrete Diffusion Models

PhD Position F/M Theory for Discrete Diffusion Models Download job offer in PDF format Contract type : Fixed-term contract Level of qualifications required : Graduate degree or equivalent Fonction : PhD Position Context The PhD position will be in the framework of the ERC Starting Grant DYNASTY (Dynamics-Aware Theory of Deep Learning). The position might include traveling to conferences for paper presentation. Travel expenses will be covered within the limits of the scale in force. Assignment Discrete diffusion models have become a leading alternative to autoregressive models for generating text and other categorical data [1, 2]. They generate samples by reversing a Markov chain that progressively corrupts the data, using a score function learned by a neural network [1]. Despite their empirical success, their theoretical understanding remains far less developed than that of their continuous counterparts. The objective of this PhD is to study the theoretical foundations of discrete diffusion models, and in particular how well they learn and generalize when the score is estimated by a neural network. Building on recent statistical analyses [3, 4] and on generalization bounds for diffusion models [5], the project will investigate how statistical, approximation and optimization errors affect the quality of the generated samples, and will validate the theory through numerical experiments. References [1] A. Lou, C. Meng, S. Ermon. Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution. ICML, 2024. [2] S. S. Sahoo, M. Arriola, Y. Schiff, A. Gokaslan, E. Marroquin, J. T. Chiu, A. Rush, V. Kuleshov. Simple and Effective Masked Diffusion Language Models. NeurIPS, 2024. [3] Z. Zhang, H. Fu, Z. Yang, M. Wang, T. Zhao, M. Chen. Generalization Bounds for Discrete Diffusion: Statistical Advantage of Masking. ICML, 2026. [4] L. Blunda, T. Farghly, U. Şimşekli, A. Durmus. Discrete Diffusion Models are Minimax Optimal Under Sparsity. arXiv:2610.19020, 2026. [5] B. Dupuis, D. Shariatian, M. Haddouche, A. Durmus, U. Şimşekli. Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models. arXiv:2506.03849, 2026. Main activities Conduct theoretical research Conduct experiments for empirical verification Write scientific articlesDisseminate the scientific work in appropriate venues. Skills Technical skills and level required : Languages : High-level of professional/academic English Coding skills : Good level of coding in Python and related deep learning libraries Benefits package • Subsidized meals • Partial reimbursement of public transport costs • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.) • Possibility of teleworking and flexible organization of working hours • Professional equipment available (videoconferencing, loan of computer equipment, etc.) • Social, cultural and sports events and activities • Access to vocational training • Social security coverage Apply for this position Share • Facebook • Linkedin • Twitter • Email General Information • Theme/Domain : Optimization, machine learning and statistical methods Statistics (Big data) (BAP E) • Town/city : Paris • Inria Center : Centre Inria de Paris • Starting date : 2027-01-01 • Duration of contract : 3 years • Deadline to apply : 2026-12-03 Warning : you must enter your e-mail address in order to save your application to Inria. Applications must be submitted online on the Inria website. Processing of applications sent from other channels is not guaranteed. Instruction to apply Defence Security : This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment. Recruitment Policy : As part of its diversity policy, all Inria positions are accessible to people with disabilities. Contacts • Inria Team : SIERRA • PhD Supervisor : Simsekli Umut / umut.simsekli@inria.fr About Inria Inria, the French national institute for research in digital science and technology, supports the French government in national research and innovation strategies in the digital field, acting as Digital Programs Agency. Inria leads over 300 research and innovation projects with its 3,500 scientists, engineers, and support staff, in partnership with universities and the digital ecosystem (businesses, entrepreneurs, and public stakeholders). Together, we explore strategic fields such as artificial intelligence, cybersecurity, quantum computing, cloud technologies, digital transformation in healthcare, digital twins, and digital technologies for defence. We develop practical solutions such as software, tech startups, partnerships with national companies, and cutting-edge training programmes. Our goal is to drive scientific, technological, and industrial excellence to ensure France’s digital sovereignty.