How do I differentiate between sender and receiver in an chat app Laravel?

I am making a private(one to one) chat app in Laravel 5.7. The problem is with schema I think. If user1 is logged in and he creates a new conversation with user2. That would be created with conversation_id=1. Next time when user2 is logged in lets assume he will be finding his ID in sender column and he won't find his ID in sender_column, new conversation will be created which shouldn't be created because for creating the new conversation we have to check in sender and receiver column both.

Here is my schema

    =======User Table========
    Schema::create('users', function (Blueprint $table) {
        $table->increments('id');
        $table->string('name');
        $table->string('email')->unique();
        $table->timestamp('email_verified_at')->nullable();
        $table->string('password');
        $table->rememberToken();
        $table->timestamps();
    });

    =============Chat Table=============
    Schema::create('chats', function (Blueprint $table) {
        $table->increments('id');
        $table->unsignedInteger('user1_id')->nullable();
        $table->foreign('user1_id')->references('id')->on('users');
        $table->unsignedInteger('user2_id')->nullable();
        $table->foreign('user2_id')->references('id')->on('users');
        $table->timestamps();
    });

    ===============Messages Table================
    Schema::create('messages', function (Blueprint $table) {
        $table->increments('id');
        $table->unsignedInteger('chat_id')->nullable();
        $table->foreign('chat_id')->references('id')->on('chats');
        $table->text('messages');
        $table->timestamps();

    });

Maybe you understand it by this.

Users                            Chats                                
id    name          chat_id    user1_id    user2_id
1     Mark             1           1           2
2     David            2           2           1
3     Henzard          3           2           3
                       4           3           2

Please suggest me a better solution.

via Chebli Mohamed