Severi Rissanen

Severi Rissanen, Markus Heinonen, Arno Solin

While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and the empirical success of coarse-to-fine modelling, we propose a new diffusion-like model that generates images through stochastically reversing the heat equation, a PDE that locally erases fine-scale information when run over the 2D plane of the image. We interpret the solution of the forward heat equation with constant additive noise as a variational approximation in the diffusion latent variable model. Our new model shows emergent qualitative properties not seen in standard diffusion models, such as disentanglement of overall colour and shape in images. Spectral analysis on natural images highlights connections to diffusion models and reveals an implicit coarse-to-fine inductive bias in them.

Severi Rissanen, RuiKang OuYang, Jiajun He et al. · cambridge

Recent research has focused on designing neural samplers that amortize the process of sampling from unnormalized densities. However, despite significant advancements, they still fall short of the state-of-the-art MCMC approach, Parallel Tempering (PT), when it comes to the efficiency of target evaluations. On the other hand, unlike a well-trained neural sampler, PT yields only dependent samples and needs to be rerun -- at considerable computational cost -- whenever new samples are required. To address these weaknesses, we propose the Progressive Tempering Sampler with Diffusion (PTSD), which trains diffusion models sequentially across temperatures, leveraging the advantages of PT to improve the training of neural samplers. We also introduce a novel method to combine high-temperature diffusion models to generate approximate lower-temperature samples, which are minimally refined using MCMC and used to train the next diffusion model. PTSD enables efficient reuse of sample information across temperature levels while generating well-mixed, uncorrelated samples. Our method significantly improves target evaluation efficiency, outperforming diffusion-based neural samplers.

Severi Rissanen, Markus Heinonen, Arno Solin

The covariance for clean data given a noisy observation is an important quantity in many training-free guided generation methods for diffusion models. Current methods require heavy test-time computation, altering the standard diffusion training process or denoiser architecture, or making heavy approximations. We propose a new framework that sidesteps these issues by using covariance information that is available for free from training data and the curvature of the generative trajectory, which is linked to the covariance through the second-order Tweedie's formula. We integrate these sources of information using (i) a novel method to transfer covariance estimates across noise levels and (ii) low-rank updates in a given noise level. We validate the method on linear inverse problems, where it outperforms recent baselines, especially with fewer diffusion steps.

Victor M. Yeom-Song, Severi Rissanen, Arno Solin et al.

Diffusion models struggle to produce samples that respect constraints, a common requirement in scientific applications. Recent approaches have introduced regularization terms in the loss or guidance methods during sampling to enforce such constraints, but they bias the generative model away from the true data distribution. This is a problem when the constraint is misspecified, which is a common issue in scientific applications where constraint formulation is challenging. We propose to integrate guidance-inspired adjustments to the denoiser, instead of the loss or sampling loop. This achieves a soft inductive bias towards constraint-compliant samples. We show that these softly constrained denoisers exploit constraint knowledge to improve compliance over standard denoisers, while maintaining enough flexibility to deviate from it in case of misspecification with observed data.

Yang Yang, Severi Rissanen, Paul E. Chang et al.

Amortized simulator-based inference offers a powerful framework for tackling Bayesian inference in computational fields such as engineering or neuroscience, increasingly leveraging modern generative methods like diffusion models to map observed data to model parameters or future predictions. These approaches yield posterior or posterior-predictive samples for new datasets without requiring further simulator calls after training on simulated parameter-data pairs. However, their applicability is often limited by the prior distribution(s) used to generate model parameters during this training phase. To overcome this constraint, we introduce PriorGuide, a technique specifically designed for diffusion-based amortized inference methods. PriorGuide leverages a novel guidance approximation that enables flexible adaptation of the trained diffusion model to new priors at test time, crucially without costly retraining. This allows users to readily incorporate updated information or expert knowledge post-training, enhancing the versatility of pre-trained inference models.

Severi Rissanen, Pekka Marttinen

Using deep latent variable models in causal inference has attracted considerable interest recently, but an essential open question is their ability to yield consistent causal estimates. While they have demonstrated promising results and theory exists on some simple model formulations, we also know that causal effects are not even identifiable in general with latent variables. We investigate this gap between theory and empirical results with analytical considerations and extensive experiments under multiple synthetic and real-world data sets, using the causal effect variational autoencoder (CEVAE) as a case study. While CEVAE seems to work reliably under some simple scenarios, it does not estimate the causal effect correctly with a misspecified latent variable or a complex data distribution, as opposed to its original motivation. Hence, our results show that more attention should be paid to ensuring the correctness of causal estimates with deep latent variable models.