Just think of it this way, the domain model should be dependent upon nothing and have no infrastructure code within it. The domain model should not be serializable or inherit from some ORM objects or even share them. These are all infrastructure concerns and should be defined separate from the domain model.
But, that is if you're looking for going for pure DDD and your project values scalability and performance over speed of initial development. Many times, mixing infrastructure concerns with your "domain model" can help you achieve great strides in speed at the cost of scalability. The point is, you need to ask yourself, "Are the benefits of pure DDD worth the cost in the speed of development?". If your answer is yes, then here is the answer to your question.
Let's start with an example where your application begins with a domain model and it just so happens that the tables in the database match your domain model exactly. Now, your application grows by leaps and bounds and you begin to experience performance issues when querying the database. You have applied a few well thought out indexes, but your tables are growing so rapidly that it looks like you may need to de-normalize your database just to keep up. So, with the help of a dba, you come up with a new database design that will handle your performance needs, but now the tables are vastly different from the way they were before and now chunks of your domain entities are spread across multiple tables rather than it being one table for each entity.
This is just one example, but it demonstrates why your domain model should be separate from your persistence model. In this example, you don't want to break out the classes of your domain model to match the changes you made to the persistence model design and essentially change the meaning of your domain model. Instead, you want to change the mapping between your new persistence model and the domain model.
There are several benefits to keeping these designs separate such as scalability, performance, and reaction time to emergency db changes, but you should weigh them against the cost and speed of initial development. Generally, the projects that will gain the most benefit from this level of separation are large-scale enterprise applications.
UPDATE FOR COMMENTATORS
In the world of software development, there is Nth number of possible solutions. Because of this, there exists an indirect inverse relationship between flexibility and initial speed of development. As a simple example, I could hard code logic into a class or I could write a class that allows for dynamic logic rules to be passed into it. The former option would have a higher speed of development, but at the price of a lower degree of flexibility. The latter option would have a higher degree of flexibility, but at the cost of a lower speed of development. This holds true within every coding language because there is always Nth number of possible solutions.
Many tools are available that help you increase your initial development speed and flexibility. For example, an ORM tool may increase the speed of development for your database access code while also giving you the flexibility to choose whatever specific database implementations the ORM supports. From your perspective, this is a net gain in both time and flexibility minus the cost of the tool (some of which are free) which may or may not be worth it to you based on the cost of development time relative to the value of the business need.
But, for this conversation in coding styles, which is essentially what Domain Driven Design is, you have to account for the time it took to write that tool you're using. If you were to write that ORM tool or even write your database access logic in such a way that it supports all of the implementations that tool gives you, it would take much longer than if you were to just hard-code the specific implementation you plan on using.
In summary, tools can help you to offset your own time to production and price of flexibility, often by distributing the cost of that time to everyone who purchases the tool. But, any code including the code that utilizes a tool, will remain affected by the speed/flexibility relationship. In this way, Domain Driven Design allows for greater flexibility than if you were entangle your business logic, database access, service access, and UI code all together, but at the cost of time to production. Domain Driven Design serves Enterprise level applications better than small applications because Enterprise level applications tend to have a greater cost for the initial development time in relation to business value and because they are more complex, they are also more subject to change requiring greater flexibility at a reduced cost in time.
