  The imputation of missing values in time series has many applications in
healthcare and finance. While autoregressive models are natural candidates for
time series imputation, score-based diffusion models have recently outperformed
existing counterparts including autoregressive models in many tasks such as
image generation and audio synthesis, and would be promising for time series
imputation. In this paper, we propose Conditional Score-based Diffusion models
for Imputation (CSDI), a novel time series imputation method that utilizes
score-based diffusion models conditioned on observed data. Unlike existing
score-based approaches, the conditional diffusion model is explicitly trained
for imputation and can exploit correlations between observed values. On
healthcare and environmental data, CSDI improves by 40-65% over existing
probabilistic imputation methods on popular performance metrics. In addition,
deterministic imputation by CSDI reduces the error by 5-20% compared to the
state-of-the-art deterministic imputation methods. Furthermore, CSDI can also
be applied to time series interpolation and probabilistic forecasting, and is
competitive with existing baselines. The code is available at
https://github.com/ermongroup/CSDI.
